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Just let them spawn every X years, for each empire, but only if their total number per empire is below Y numbers or something. Nearest empty system would always have something to do.
 
Pirates are more or less a kind of spawned monsters, not a real AI faction (basically they are tied to the Empire that spawned them). We can however toy with the fleet they spawn so they use more variety of weapons and upgrade to better designs as the game go on. The problem right now is how to make them respawn after the player kill them while not making them an impossible task to beat.

Perhaps make them a recurring problem, but one you can defeat for good with some kind of special project? Or just make it so that enacting the Social Welfare Programs edict cuts the number of malcontents down to such a degree that not enough people are tempted to go pirate, thus preventing pirates from reappearing when you have Social Welfare Programs up and running?