Changes in Arnor

Arnor would be one of the main battlegrounds for coming ethnic strife. The area would become host to a wide reaching group of refugees that would come to overwhelm the local inhabitants. At the same time this is happening, Aragorn would have claimed the throne and reunited it with Gondor. So we would see a mix of conflicts. The first would be between the various and frequently hostile refugee groups. Then, there would be conflicts between them and the locals. Lastly, there would be conflict between the government on one hand and a population who had no effective government for centuries.

The Conflict

Prelude

Gondor's rule would be shaky. Extremely shaky. Its leader is replacing a family that had ruled for generations. The elites Aragorn would need support from would be the old nobles. The same people whose power came from their loyalty to the people Aragorn replaced. But Aragorn's preexisting support base comes from Rivendell and Arnor. One is a foreign power. The other has no formal state structures to rely on and is too poor to supply useful funds.
But this rule will exist. Remember, Aragorn reclaimed the title of King of Arnor first. Which grants him power over everything between the Misty Mountains and the Blue Mountains. So not just Bree but also the Shire. There effectively little there to work with.
At best there is a company of "hobbitry in arms" and 12 hobbit police officers for the entirety of the Shire. The rest is the realm of the Northern Rangers. Bree and the two other tiny towns near it would have city administrations that govern there. So Aragorn would have to effectively import an administrative apparatus to an area where there is none. And the area he has the resources to take from he has also shaky control.

Deployment

So, the main movements into the area that we need to keep in mind are the refugees from the rest of Middle Earth. First there would be the Wild Men. The pressure from Rohan would naturally drive them from Rohan's territory. Especially after their alliance with Isengard. They would follow Saruman into Arnor out of loyalty or flee from genocidal persecutions by Rohan. Either way, we can expect them to form one wave. Due to the wars to the east and how close Arnor is, Arnor would look pretty tempting as a place to resettle.
Next there would be Gondorian civilians. The fighting would hit a huge proportion of Gondor's territory - including Gondor's biggest cities. Many would flee the fighting. More importantly, returning would prove difficult. Their farms, houses and shops would all be destroyed. Especially after the reintroduction of the Great Plague during the attack on Minas Tirith, the area would be dangerous to move back into. Even if there was hope for rebuilding their lives. Arnor seems like a good place to relocate.
At the same time, the refugees displaced by the Easterling invasions in their norther campaign would probably flee with them. Thus, the displaced Northmen would form a separate but related group. These would probably be a higher proportion of the original prewar population of Rhovanion due to the more extensive devastation compared to Gondor and more limited state structure to provide aid. Gondor is weak, but like Arnor, Rhovanion has virtually no real unifying government.
Next would be the emancipated slaves. Of which there would be three main groups. The first would be those from the Lake-town Underground Railroad. It makes perfect sense to have their final destination be Arnor. There is the possibility that after Lake-town is set up, you would see a slow increase in smallholder farms and villages set up in the area by escaped slaves fleeing the Easterlings. They would probably be somewhat incorporated into the area already an living peacefully with the natives. Granted, there is likely to be some tensions - there always are between a local population and those seen as "alien" or "outsiders". But they are likely to also feel threatened by the new inhabitants coming in huge numbers, desperate and competing for scare resources.
The last two groups of slaves are those from Nurn and Harad. Naturally there are going to be plenty of slaves in these areas who want to escape the lands they were enslaved in. Even if they are no longer enslaved, the memories would make the area a reminder of their trauma. Not to mention they would still be living next door to the dis-empowered former masters. In the case of the Southrons, slavery would be replaced with sharecropping. This for all practical purposes is slavery by another name. Perhaps with fewer beatings and the legal right to marry, but still understandably too close for comfort for recently freed slaves. For both groups, anywhere with better opportunities would be attractive to them.
Then there is the Grey Company we have to look at. It is part of the forces of Arnor. But it was active at Minas Tirith. Personally I would send this force to Isengard. Their objective would be simply be a caretaker force. Ideally, they would just begin repairs to the facilities and inspect its contents. Then, Aragorn would invest more time and money based on what is found and when resources are available. It would also keep the area from falling back into Wild Men control.

Battlefield

We need to remember the scale of the territory Aragorn is attempting to control here. The events I talk about in the other sections on Gondor would have extended Gondor's territory to where it was at it's peak - 1,203,200 sq. miles. But Mordor would have come under Gondor's rule as well - adding another 140,000 sq. miles.
Arnor adds an additional 248,540 sq. miles. But The Shire is 21,400 of that. These two regions - the human and hobbit areas - would pose unique challenges for a regime already extremely taxed by radical expansions of territory elsewhere. The human areas will meet essentially no opposition to nominal control by Gondor but will be hard to solidify the administration. The Shire meanwhile would not resist and is actually quite well adapted to self government that virtually no effort would be needed in retaining control. But it is controlled by Saruman. Which increases the cost of taking control.

Conditions

One element we need to keep in mind here is that the Shire would be its own battlefield at this point. It is around this time when Saruman's occupation of the area would be coming to a head. The aid coming from Gondor would come in the form of the Fellowship Hobbits. Their connection to the established traditions and political posts in the Shire give them legitimacy.
This is especially true due to Aragorn's backing. The posts the Fellowship Hobbits occupy derive their authority from the power of the King of Arnor. The same position that Aragorn now claims. Essentially, the Hobbits would have a pretty water tight case. The Reunited Realm would effectively be able to secure its claims here quite easily after Saruman is expelled. Which basically means that all Aragorn would have to do is keep the outside chaos from spilling over and at least one area would be solidly under his control.
Next are the Easterling Whites after their defeat. And this would be the main cause of the problems. Rhovanion would not be safe, as we have already discussed elsewhere. But the area they would have to move into next would be inhabited by their former slaves. Plus refugees from their atrocities in the recent invasions the Easterlings initiated. The Northmen would not take too kindly to this. The best defense they would have is that they did not lead or order those crimes.
The slaves and Rhovanion refugees would probably not be too convinced. After all the Auxilia forces behind the Whites benefited from the old regime. They still participated in those conquests even if they did not order them. Plus, the whites still waged civil war to establish essentially a moderate version of that same regime. So they might not be as bad as the old elites. But they are essentially the same people that many fled from.

The Engagement

At this point, the goal would be to institute some form of state building and economic development. The land grants I propose going to soldiers would be an extremely valuable tool in that. It would essentially lead to importing already trained and equipped troops into an area. Through the land grant system, this not only provides domestic security and the seeds of economic development of the area.
But we have to recognize that this would be limited. This military based resettlement program would need to be applied to the entirety of Gondor's border areas. In fact, it would probably be better to focus on those areas first. So the men sent here would be much lower than what the land could support. Possibly also far below the full demands of the region. We have to remember this is a huge region.
There would be two possible work arounds. First, Bree and the Rangers. If the locals are able to be converted into the foundations of the administration, a lot of potential conflicts could be avoided. As Bree is the main city, it makes sense to make it the regional capital. The infusion of jobs in construction and trade that would spur means that the initial residents would see their economic fortunes rise. Demographically, they will be reduced in significance. But they will rise to the top both economically and politically.
The Rangers would fill the same role, just militarily. Most likely they would initially just get increases in budgets and official training from Gondor. Possibly, a radical increase in powers too. Over time, they would likely become more of a traditional officer corps. The old Rangers would become the organizers of local militias. From this, they would likely become military families whose children embrace military service due to it being the only thing they know.
One of the clearer uses of the Rangers involves the Grey Company at Isengard. It was only 30 people. Granted, this area would be relatively peaceful given that no major military powers were in the area. But still, this would not be ideal in the context of ethnic strife, weak government control and so forth. So I think the Grey Company would organize 2 companies of militia. This would turn the 30 Rangers into a force of 152. This is a much better number.
And it would be extremely useful in this area. Isengard would be perfectly placed to stop Rohirrim from chasing after Wild Men into Arnor. So enough men here to fully control passage would be vital. This then would see a major settlement arise at Isengard. The 152 men now in the militia would be working age men only part time in the military. This would mean that they would be prime candidates for land grants in the area. Which in turn brings families. If the averages I found are kept, this means between 608 and 912 new people in the area.
With peace now imposed and rising population we can expect growth of industrial and trade activity. This pass is a natural trade route between Rohan and Arnor. The libraries and established factory space in Isengard means industrial capital already in place. Now it is just a matter of using it. Then, it is also much closer to Arnor's now growing consumer base than Gondor's other industrializing centers. We can expect Isengard to become a major factory now.
Also important here is the influence of cannons. It seems logical to me that the factories in Isengard would be the first specializing in artillery manufacturing. Which was a critical factor in the ending of Feudalism. Basically only the central authorities could afford to make and deploy cannons. Nobles had one main advantage in resisting central authority - namely castles. But cannons are quite effective against castle walls. So nobility lost one of its most important military positions.
Just as important as the political changes is the technological changes. Once cannons get adopted by Gondor, two major ones will follow - guns and star forts. Guns are a logical extension of cannons. Take a early cannon, shrink it enough to be carried by hand and you get a very simplistic view of early guns. They were more expensive to make but easier to train soldiers on and maintain. So once the initial investment is made, the same gun can be used by several generations of troops if cared for right.
And yes, there were actual battlefield improvements for early guns over bows. Yes guns were less accurate and had shorter range. But they caused significantly more gruesome injuries to those that were hit. So a non fatal hit was much more likely to cause a loss of a soldier than an arrow. Then, there is the noise issue. One gun may not make as much noise as a cannon, but they are a lot more common. Which leads to incredibly noisy and smoke filled battlefields. Especially against troops not used to this, it can be disorienting and cause panic. Remember - it does not matter if the enemy soldier dies, is captured, flees or is incapacitated from disease or injury. What is important is that enemy is no longer fighting.
The other development I mentioned is the star fort. This was an Italian creation named for the shape of the forts. Key changes involved the lowering of the walls and sloping them outwards so that cannonballs would not have as much of an impact. The use of earthworks and a slope either deflected or dissipated the energy of the bombardments much better. Triangular bastions protruded out from the walls such that guns and cannons could be fired out at enemies approaching the walls. These then replaced the traditional towers. Such forts grew to have networks of triangular, smaller forts placed outside them to create a complex and overlapping fields of fire.
So as castles become obsolete because of cannons, star forts will become the new norm. I suspect that Isengard would be the center of this. First is the discussed role of Isengard in producing the new weapons. So the garrison would likely be the first to adopt the new weapons and first to need to defend themselves with them. Plus, they will be the best place to experiment with not just improvements in the equipment but also how to best use them and counter them. So Isengard is likely to see its defenses altered such that it becomes the first star fort. From there, the use of star forts will expand to cover other strategically valuable areas.
The other major tool for importing control is civilian land grants. I'll be borrowing from Russia again partially because that is what I am more familiar with. But many nations instituted similar policies. The Russian version under Nicholas II involved 16.5 hectares of land per man settling in Siberia. But not just that - the government wanted them to become the profit oriented and politically reliable. So a host of other supports were granted. These included affordable lines of credit extended to peasants. There were education programs on new farming methods and means of land improvement. There were exemption from taxes and even a small subsidy.
If one is trying to induce settlement, this is a solid means of doing it. Between 1890 and 1914, these policies led to 10 million people moving to the areas covered. The full package of incentives were offered in 1906. Between 1908 and 1913, 2.8 million of those people decided to move. This effectively increased the population east of the Ural Mountains 250%. Which means that this is a pretty solid means of getting people to go where the government wants them to go.
Which means that this would be perfect for Gondor. It has a huge population of destitute people and recently liberated serfs and slaves. Plus, as mentioned, a lot of unsettled land. Now, some of this land is going to be in areas retaken in Harad and Rhun. So some of this resettlement would be in those areas. But due to security concerns, I suspect that military land grants would be the focus there. Not to mention that is where most of the devastation, poverty and existing populations would already be. So most of the need for people would be in Arnor and thus the reliance on civilian land grants.
Riasanovsky, Nicholas V. (2000). A History of Russia (sixth edition). p. 432.
Now, the question becomes how this mix begins to work together. Or more importantly, would the new residents even get along at all? Lets be honest here for a second. This is a realm that I am less familiar with. So I am less certain of my predictions. But at first, the expansion of land grants and promotion of the local inhabitants in the local administration would at least mitigate some of the problems. I doubt conflicts would disappear. Just limited to the shadows and the fringes - such as secret societies or isolated extremists. If this would be met with government contracts going to the local gentry, then all of this would see everyone experiencing rising living standards. So it is less likely that other ethnic groups would be seen as threats to survival.
But the arrival of the White Easterling remnants would change this. The sudden introduction of this population in an already strained society would probably not end well. The Easterlings for their part would have several troubling issues. First, they are desperate. After a long march away from their homeland on which they were probably harassed by their enemies, they would need a safe haven. Secondly, they would likely have their weapons left and have a history of solving disputes with force. Most recently, this manifested in a humiliating defeat in a war of conquest that naturally would have alienated the same people they now are seeking to integrate with. The civil war was the product of their failure and the reason for their need to find a new home. Anything that grants them safety, security and a means to regain some glory would be something they would gravitate towards.
Then, you have the established locals. Who already have differences and tensions. Hidden under the surface, yes, but still there. Meanwhile, the same policies that led to the submerging of these differences would include the militia system. This led to the importing of central Gondorian authority to the area as best as could be expected. But at this point we cannot expect this to be all that firm. An improvement to be sure, but not good. The result at this point would be a collection of armed men, with little centralized control and a new enemy.
This enemy entering their homeland just recently committed atrocities against their friends and family. In the service of Sauron. The conflict would probably start with some localized dispute where the Whites try and set up a new settlement. This will produce conflicts with the locals. The people facing the dispossession or at risk of it would be newly set up civilians fleeing Mordor or the slaves with centuries of grievances against Easterlings. In this atmosphere, a wrong move by either side is both extremely likely and would result in a rapid escalation of hostilities.
It seems entirely logical that the newly formed militia would take the initiative and attack the White Easterlings. I would expect some form of localized clashes break out that escalates into full war as the rest of the militias rally to the area. At the same time, the Easterlings would be so battered from the previous conflicts that they would struggle to survive. While they would likely be able to inflict a lot of damage on the militias and civilians in the area, I doubt they would be able to win.
They would be trapped against the Misty Mountains and killed. Or they would try to go between the White and Misty Mountains. But Isengard has its own garrison now. This force would try and stop them. Which might be the first instance of guns being used in Middle Earth depending on the exact timeline. But lets say they do get through somehow. The Rohirrim would also not take kindly to them either. Their only hope would be for Aragorn to intervene.
Well, this is technically possible. The Southern Fiefs did not have near the direct exposure to the atrocities of the Easterlings. So the passions would be less strong there.

Outcome

The real problems come soon after this. The state control over the area would be much better than it was prior to the reign of Aragorn. But it would likely take the majority of his reign or possibly that of his successor to fully solidify. Especially with the Rangers as the officer corps of the militia having a long tradition of independence. These militia groups also were just mobilized to engage in ethnically motivated fighting.
Which means a major line has been crossed. These militia units could now turn on each other. The ethnic conflicts that were hiding beneath the surface previously could become the basis for continuing strife. Instead of demobilizing after defeating their external foes, war against their internal ones could be next.
The Rangers would have difficulty containing this. Their traditions of independence means they could see such disorders as a way to increase their own power. Both the officers and rank and file men would see the opportunities as a tool to settle scores, eliminate rivals, escape debts or kill witnesses of their crimes. Property of their enemies could be seized to make everyone involved richer. Not to mention that such conditions escalate hatreds and anger by a significant amount - a powerful force on its own without ulterior motives.
Then there is the negative incentives that make the containment difficult. Attempts to restrain the violence once it gets unleashed opens the person up for charges of betraying their community as defined by the extremists. Or appearing weak to the enemy extremists. So if an officer attempts to restrain their men, they might get murdered for their efforts. Or the attempts to negotiate with rival militias becomes the setting for them getting massacred. Which then makes it seem to the officers the only way to survive is a successful defeat of their enemies. Essentially artificially escalating the conflict.

Aftermath

Which then suggests to me that the only way to prevent full fledged social disintegration would be Gondor calling in its established professional military force. The elves from Lindon or Rivendell might be called in to provide aid too. Some of these would likely be the force mobilized to help liberate the Shire.
So, the elves, again, would have humanitarian interventions as a justified in their international relations doctrine. Two of the major elven kingdoms border the territory in question. One has marriage relations with the internationally recognized king and the other is already operating in the area with permission from that same ruler. Aragorn would have little interest in watching his kingdom tear itself apart through ethnic conflict. This is both a threat to his childhood home and his power. So elven intervention and reinforcements from Gondor's professional troops would be swift. Which on the positive side, the fighting would be minimized.
The interventions would probably be brutal too. At least on the part of the Gondorians. Aragorn would want to make sure that the situation gets under control as soon as possible. But this would probably justify in his mind the use of heavy handed tactics involving martial law, a strong police state and large garrisons to impose law and order. This will certainly clamp down on the fighting. But would probably lead to disillusionment with the elven allies.