There are reports about a potential fourth Star Trek film, with some outlets suggesting that Zachary Quinto has reached out to J.J. Abrams about the project. However, there is uncertainty about the status of the film, as one report claims that Paramount has moved on from a sequel in the Kelvin timeline. J.J. Abrams has reportedly found the story for a potential fourth film to be compelling, but the project's current status is unclear.