Dragon Claw

The ancient dragons used to rule the world. Their First Empire did that for more than 10 000 years, in fact. At least partially it was caused by naturally dominant minds of the dragons - they were simply unable to not be on the top. The entire First Empire had every single ancient dragon out there rule over entire city of mortals that worshipped them as their gods (enough to satisfy their blood's cravings), and because no ancient dragon could hope to remain alive after enraging the Eldest Dragon, the de facto emperor of the First Empire.
You don't rule the world for 10 000 years and then die out without leaving a trace. Sure, the ancient dragons are most likely extinct (or at least none of them was seen in Karadia for many millenia), but the dragons are still there. High Dragons might be too troublesome, and the lesser dragons are pretty much animals... but there are also the greater dragons. Who, while still being mostly animals, inherited many of their ancestors' instincts. And are both more powerful than the lesser dragons and sometimes unexpectedly intelligent.
The Dragon Claw can be seen as a reenactment of the First Empire done in modern Lost Lands. Sure, the dragons don't talk even remotely as much as they used to back then, and their followers tend to be on the barbaric side of things. But the rest, is the same. The dragons are worshipped and allowed to amass a hoard of sacrifices (that they don't even use for anything, it's just something that satisfy their deep instinct for control and ownership) in exchange for occasionally pulverizing someone who dared to attack their followers.
The Dragon Claw is often considered by the Empire to be the uglier cousin of the Nine Hordes. Sure, sometimes they are tribes that can be reasoned with. However majority of them only dreams of conquests and pillaging of things, many dragons are downright mean by nature (despite their sapience being questionable), and some of the forms of worshipping are downright bizarre and sometimes squicky.

Structure

Dragon Claw is in an essence a wide variety of tribes who grew a bit too immersed in the process of offering a tribute to the nearby greater dragon in order for it to not attack them (and instead sometimes attack those that the tribe pointed towards to) and turned that into religion. The tribes are almost always widely different from one another when it comes to their structures, and the only common factor is that there is always some small, closed priest caste that is the only group that's allowed to enter the dragon's lair, offer it the sacrifices and ask it for its help in something.
The tribes in question are of varied ancestry. The most common cases are the mountain elves, some more primitive beastkin and occasionally some goblins. The difference between the species in question greatly influences the forces of the Dragon Claw in their area. Mountain elves are typically the most organized, beastkin are the wildest and fiercest, and the goblins are plain crazy (especially when they have horgoblins among their ranks.

Military

The Dragon Claw typically fields a standard assortment of tribal warriors, skirmishers and some more primitive spellcasters that are either more mage-like or more sorcerer-like. There is also the priest caste who is blessed with a sliver of their dragon's natural magic power. The result is a bit unique form of magic resembling a very primitive theurgy, that allows them to use a wide variety of buffs and magicks that are rather dragonic in theme. This is believed to be something that the greater dragons inherited from their ancient dragons ancestors.
Extremely successful warriors of the Dragon Claw are sometimes allowed to use the dragonic progeny (wyverns or drakes) as mounts, tamed through the will of the greater dragon. Anyone else who would try to mount them would be immediately devoured. There is also the greater dragon patron of the tribe to be considered, since if he decides that his worshippers are in sufficient danger, he will act. And slaying a greater dragon is extremely hard.