Does Kanan crew ability trigger after gaining stress from crossing a debris or before?

Can I pull a white move over the debris, get the stress, use Kanan and then perform an action?

Good Question!

Debris clouds cause stress AFTER the "Check Difficulty Step".

Rules Reference P13

"While a ship executes a manoeuvre, if it moves through or overlaps an obstacle, it executes its manoeuvre as normal but suffers an effect based on teh type of obstacle:

<snip asteroids>

Debris Clouds: After the Check Difficulty step , the ship gains 1 stress token. After executing the manoeuvre, it rolls one attack die. On a *Critical* result, the ship suffers one *Critical* damage.

Kanan Jarrus (Crew)

After a friendly ship at range 0-2 fully executes a white maneuver, you may spend 1 to remove 1 stress token from that ship.

It's possible, as the Check Difficulty step comes right before the action, which means that you will have both fully executed the manoeuvre and completed a White manoeuvre.

I'm going with yes, as both effects are added to the ability queue at the same time, with game effects like the obstacles being forced in first, leaving Kanan to activate afterward.

there is already a topic in this forum which clarifies this.