Slitherine

A unit of light cavalry is in skirmish and evade due to a charge of heavy cavalry.

The light cavalry is nevertheless contacted according to the rule the unit lost a level of cohesion and retire of 4MU.

my question is: the light cavalry become spent or not?

No. There was no combat and your light cavalry didn't take a hit - it just lost cohesion as it had to evade even more than it thought it had to.

Being spent only occurs if taking a hit in combat or receiving 4 hits in the assault phase when the target the cavalry is charging fires.

thanks