The news surrounding Star Trek sequels have lately revolved around the "will he or won't he" of Quentin Tarantino's R-rated film. That film is still in the works according to Paramount's Jim Gianopulos, but as it's a long way off it will be preceded by Clarkson's true sequel to 2016's Star Trek Beyond.
This will mark Clarkson's return to feature filmmaking after making her directorial debut with 2010's Toast, which starred Freddie Highmore. Plot details on her film are slim, but the script by J.D. Payne and Patrick McKay Chris Hemsworth as Captain Kirk's father, who sacrificed his life in the opening scenes of 2009's Star Trek. So you can definitely expect to see Chris Pine return, as well, and Zachary Quinto is signed for another movie. The rest of the cast aren't on board yet but that is likely to change.
Here is the early plot synopsis for Star Trek 4: “In the next installment of the epic space adventure, Chris Pine’s Captain Kirk will cross paths with a man he never had a chance to meet, but whose legacy has haunted him since the day he was born: his father.”