The Cloak and Intercept mission allows any Birdmen starships (ones with a cloaking device, of course) to remain cloaked while performing an intercept. If your starship sets its Primary Enemy to match your intercept target, it will engage that one starship in combat before the regular combat phase. If your starship survives that combat and has no damage, it will immediately recloak and set its Primary Enemy to None.
If the starship does not have a Primary Enemy set or it is set to a player other than the intercept target, the starship will intercept and remain cloaked if it can. In this case, it will not initiate combat.
It is important to note that any starship which loses its current active cloak during an earlier portion of the turn will not recloak at the end of combat. If the starship takes damage during the combat, its Primary Enemy will not reset to None.