The director of "Star Trek 3" remains a mystery at present time, but not the film's screenwriters. According to THR, Alex Kurtzman and Roberto Orci, the writing duo behind the first two films (albeit with help on "Star Trek Into Darkness" from Damon Lindelof), will write "Star Trek 3" for Paramount and Bad Robot.
Whether Kurtzman and Orci, who also wrote the scripts for "Transformers," "The Amazing Spider-Man 2" and "The Edge of Tomorrow," would return for another tour of duty on the U.S.S. Enterprise was up for debate as recently as last month. A July 22 report from Badass Digest claimed that Ashley Edward Miller and Zack Stentz ("X-Men: First Class" and "Thor") were on the verge of being hired for the job. Per THR, Miller and Stentz were discussed for the project but apparently Paramount decided to go with Kurtzman and Orci.
For more on "Star Trek 3," and why Kurtzman and Orci were tough to lock down, head to THR.