According to ComicBook.com on Dec. 6, it appears that both J.J.Abrams and Damon Lindelof will not be taking part in writing the script for "Star Trek 3". In fact, this task will be assigned to Roberto Orci who had co-wrote the first "Star Trek" and "Star Trek Into Darkness".
Following that, the remaining to writers will be J.D. Payne and Patrick McKay who had been known to work with Abrams on a script adaptation of "Boilerplate". This is a story based off a graphic novel written by Paul Guinan and Anina Bennett which Abrams hopes to later produce.
Even at this point the "Star Trek 3" film still has no director assigned. Abrams will be too occupied with working on Disney's "Star Trek VII" but there is rumor that there is a favored writer by the name of Joe Cornish who had also directed "Attack the Block". Abrams even admits to Cornish as being a favorite of his and hopes to see him involved in such a project.