This is probably group and system dependant. I'll often outright narrate changes in my characters priorities happening, normally as part of outcome narration. I think it's so group dependant because of how these priorities are established in group understanding in the first place and how attentive the group is to them. It's one thing I've noticed a lot of OC players are good at. Of course certain systems like Burning Wheel or Dungeon World flat out have you write them down.
Although I've still got a nagging feeling we might be talking past each other given the Burning Wheel example. Do you establish something akin to beliefs in all games, even if they're not formalised? I think I do for most of them.
I don't know if I'm following your account of "priorities".
If a character flees in fear (whether due to a failed Steel test in BW, or a failed morale check in Traveller, or whatever) I am assuming that we are now saying their priority has changed - to saving themself - and we are seeing what follows from that change in priority. In other words, I am taking it that
priority =
motivation for action. I took this to follow from the idea that declaring an action - say, in a system that doesn't use Steel or morale, declaring that my PC flees in terror - expresses a characters priorities.
But in BW this wouldn't necessarily require rewriting a Belief. (Contrast to Pendragon, where it would likely require adjusting the balance between Valorous/Cowardly.) In BW Beliefs are principles/commitments/ideals, but not necessarily
actual motivations - it's up to the player to choose how to incorporate or respond to their Beliefs in the motivations they attribute to their PCs.
So when I asked about
changing priorities, I was asking about - say - how a player would decide that now is the time that their brave, or ruthless, or etc, character decides to hesitate/run away/etc. (In the Cthulhu Dark case, it was a normally sensible character - a butler - screaming in panic and calming his nerves by drinking laudanum.)