The Birdmen Cloak and Intercept mission allows any of your starships with cloaking devices to remain cloaked while performing an intercept. If your starship sets a Primary Enemy to match your intercept target, it will engage that one starship in combat before the regular combat phase, then set the Primary Enemy to None. If it survives that combat and has no damage, it will immediately recloak so it will not enter combat with any other ships or planets.
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, but it will not initiate combat.
Any starship which loses its current active cloak during an earlier portion of the turn will not recloak at the end of combat.
See also: Out of Fuel.