Provincial is effectively left entirely to the Provost. It's one of the perks of being the top administrative power in Trib. I might offer an opinion if someone is entirely unqualified, or if they have a history of errors, etc. but it's otherwise Provost's discretion.

Justiciar/Vindicator are imm-chosen. People can, and I encourage them, to announce their intent to aim for one of these. It helps me know that I should be watching you for X or Y behavior, which I might not otherwise be scouting. Provost can absolutely contribute and say "I think this person would make a good X", and I'll take that as a vote of confidence, but the final decision is an imm one.

General expectations, with exceptions and general possible differences between chars:

Provost/Provincial: Following the laws, following the Magistrate rules, on duty time, Trib-like interactions, generally not sucking.

Vindicator: Everything involved with hunting Tribunal enemies. PK skills, chasing, scouting, raiding matter here. I don't really care about your on-duty time for this. I'd highly suggest reading the Magistrate Library Vindicator notes, plus the Vindicator scroll in its respective room.

Justiciar: Everything involved with investigations on crimes, and 'legal judgment'. On duty time matters a lot. Are your warrants accurate? Do you follow the rules to the letter? Do you correct other people? RP matters here. Similarly, read the library entries and the respective room scroll.

If I see someone doing the part in outstanding rp-fashion, it's easy to know they're interested. But since that can be hard to notice, or not easy to translate, I very much suggest a general announcement of "This is what I am aiming for" / "This is my ambition" type thing in a note/role.

As a fun side note. Goodies tend to have a hard time getting Vindicator, and evils tend to have a hard time getting Justiciar.

-Ish