On current plans, at the end of Game IV, the Thaumatarch will fall–though many of the key decisions in that game will already be governance decisions, over the bits of the former Hegemony where your rebellion holds sway.
Game V will be all about consequences post-Hegemony. The war between major factions and outside powers will be a big part of it, but the governance theme will be an even bigger part, with you grappling with the responsibilities of being a rebel who won.