Orci is continuing his involvement with the franchise, after previously writing the first two Star Trek movies with Alex Kurtzman and Damon Lindelof.
Payne and McKay have a working relationship with Star Trek into Darkness director Jj Abrams, having penned a big-screen adaptation of the graphic novel Boilerplate.
Abrams will not be returning to direct the currently-untitled third Star Trek movie because of his commitments to Star Wars Episode 7, but will stay on as producer.
Attack the Block's Joe Cornish and Rise of the Planet of the Apes filmmaker Rupert Wyatt have both been tipped as potential directors for the movie.
There is currently no release date scheduled for Star Trek 3.
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