It would be kind of irresponsible to just up and leave post of High Inquisitor (or whatever) right when the crisis is over. The Inquisition would have to settle in the post-Breach world and find a purpose. It would be a bit chaotic to just suddenly disband the whole thing after taking over so much land and resources.
Possibly make it The New Templar Order as was said earlier.
Maybe slowly fade to just be some clandestine order like Cerberus or the Wardens, or slowly disappear entirely.
Guesses for possible outcomes for the Inquisition: Rule Orlais, Fade Away, New Templars, Lead Exalted March North (Tevinter or Qunari), Sacrificed For Inquisitor Ascension into a Fade Lord or Whatever, Eventually Destroyed by Nations (over time if not having a necessary purpose, who wants an independent, militant, and well armed faction in their lands?), Joins the Wardens, Becomes International Trade Guild, and I don't know what else to guess...