The only thing necessary to form a galactic empire is a galaxy wide war, perhaps against Andromedan invaders. The only way to form a defense is to cooperate on a galaxy wide scale, using shared algorithm strategies so you can coordinate attacks/defense without FTL communications.

For example, there could be a preplanned contingency to coordinate an attack on Sirius on particular years, if it's taken over by the enemy. Or preplanned priorities to counterattack on Luyten's star first, if both Luyten and Barnard's star are taken over. These plans of action allow the Empire to coordinate without ridiculous multi-decade light speed delays.

The individual star systems would mostly live independent lives, but in all matters involving "The War", devotion to the Empire's plan takes priority. Any attempts to deviate from the plans will lead to defeat by the enemy and possibly even punishment by the Empire itself. Self interest in the face of the common threat will keep everyone in line.