Great advice from Shaun Hayworth:
I think that beliefs work best when the session has a clear situation that needs to be resolved. It gives everyone something to hang Beliefs on. It’s why I hate doing the thing where you pick the next session up exactly where you left off the previous session.
Even if you can’t feasibly skip time in the fiction, restating what this session is going to be about is super helpful for beliefs.
Taken from from a conversation on the Burning Wheel Discord server on ways to lower the effort required for players to rewrite their characters beliefs for current session, and for GMs to be able to build a session off those beliefs.