Following only applies to grogs and companions. They can get 30+ XP per year for 10 XP per season for three seasons[1]. Anything over 30 xp is based on whether or not the character is involved in adventures. In the case of convelescence, XP should be spent on non strenuous abilities, given that the character is in play, and at a covenant, it is possible for characters to pick up academic abilities during convelescence, if someone is able to teach them.
This does not apply to specialists or anyone who isn't fully statted out. Specialists will advance much more slowly, based on a formula to be explained below.
[1] This mimics the wealthy virtue, and since the covenant is wealthy this makes some sense.