Simon Kinberg has been part of the X-Men franchise since X-Men: The Last Stand, as a producer, writer, and overall creative force. It's fair to say he's been as big a part of these movies as Bryan Singer, although the one thing he's never done is direct. In fact, he's never directed a feature film in his career. That may be about to change with the next X-Men movie which appears to be gearing up.
According to Collider, Kinberg is in talks to direct the next X-Men film, rumored to be titled X-Men: Supernova. The script by Kinberg calls for the return of Sophie Turner as Jean Grey, and yes it will give us the "Dark Phoenix Saga" or some version of the classic comic book tale.
This would be a big step up for Kinberg, but at least we know he's got the inside track on these characters having been around them so long. According to Turner we could see filming begin this summer, and it looks like James McAvoy could be there, too...