Kanan Jarrus (crew) reads: Once per round, after a friendly ship at Range 1-2 executes a white maneuver, you may remove 1 stress token from that ship.

Loose Stabilizer crit reads: After you execute a white maneuver, receive 1 stress token.

My ship has Kanan as a crewmember and I receive the Loose Stabilizer crit. On my next turn, I perform a white maneuver, and Kanan's ability has not yet been used this round. In what order does the above happen? Do I clear Loose Stabilizer's stress, or does Kanan go off before I get the stress?

I think it's simultaneous order, so can be in any order you like.

But maybe it would apply rule, were worse effect takes effect.

Good question, maybe you need to contact FFG for this.

PS. Now thinking, if you execute a red move, you also get it later, after Kanan ability. So maybe it's similar.

You resolve them in the order of your choosing because they have the same timing. So gain stress first, then clear with Kanan.