Every Personality card says when it can be played. Most can be played at any time. For example, you could play a Soother to reduce a Problem’s Urgency right before it erupts, or play a Coinshot to discard an Advisor right before its owner collects resources for the turn.
Cards that may only be played on your turn can be played at any time during your turn.
Only Sly Personalities may be played to affect a deal after it is closed.
Personalities are resolved in the order they are played, and each must be resolved completely before another Personality card is applied. For example A player targeted with a Seeker — a Personality that lets you look at another player’s hand and steal one of their cards — cannot play any of their cards before one is stolen.
There are a couple exceptions to this rule: Hazekillers can cancel another Personality card as it’s played, and Smokers can redirect the effects of a Personality card as it’s played.
When two or more Personality cards are played at the same time, or so close to each other that your group can’t definitively say which card was played first, the cards are resolved in clockwise order, starting with any card(s) played by the Active Player.
You may not take back a Personality card after it is played. This is true even when you play a Personality card during a deal that doesn’t close, or when two players play cards at the same time that don’t interact as expected.