Conclave
History
A calling of a conclave is a Camarilla tradition, the details of which are codified by the Inner Circle. In essence, any Kindred of sufficient standing can petition for a conclave to be organized. If a Justicar sees sufficient reason they will give permission for a conclave to be held, and officiate at the event.
Most conclaves are called to deal with a serious issue or grievance of some kind. However, because of ancient tradition, any Kindred can then bring any sort of grievance to the attention of the Justicar once the event has formally started. Not even the dumbest neonate would willingly waste a Justicar's time, but this can effectively become a multi-day affair. The Justicar acts as judge, jury, and if necessary, executioner.
Execution
A conclave is never a short affair, though it can last anywhere from between a handful of days to several weeks. It is typically held in as secure and elegant a venue as the organizing Kindred can imagine. Taking the taste and preference of the attending Justicar into account is wise, for obvious reasons.
In modern times, security has become even more of a concern. Most Justicars now have exceedingly stern demands, with some only accepting a petition once one of their own Archons has thoroughly inspected the domain and venue.
Participants
Without a Justicar, no conclave is held at all. They will often bring their own security, but a key role lies with the domain's Sheriff and Keeper of Elysium. Both will have to pool their resources to the ensure the event goes off without a hitch.
The domain's Prince is likely also present. No Prince is ever truly glad with a Justicar's presence. They are either a necessary evil for an issue that the Prince cannot handly by themself, or a very unpleasant surprise sprung upon them by an elder in the domain. Even if the Justicar is not present to deal with the Prince themself, any Prince who has a conclave organized in their domain without their own permission will lose a great amount of status.