Well, as you can see above, there was an official "passing of the torch" over at Fox today, with former X-Men movie architect/director Bryan Singer handing the reigns over to Kinberg.
Of course, this was all just pure symbolism, as Kinberg and Singer have worked side-by-side in the X-Men movie universe for many years. However, Kinberg truly is getting his first real shot by directing a massive (and pivotal) movie like X-Men: Dark Phoenix - so hopefully he has soaked up a range of great filmmaking tricks from the directors he's worked with. That list includes Edge of Tomorrow's Doug Liman; District 9' Neil Blomkamp; and Deadpool's Tim Miller.
X-Men: Dark Phoenix will be a direct sequel to X-Men: Apocalypse. The film will take place in the 1990s and will be inspired by "The Dark Phoenix Saga," the most popular X-Men story of all time.
Fox attempted to adapt "The Dark Phoenix Saga" once previously, in X-Men: The Last Stand. The attempt was not well-received by fans.