Even before the last Star Trek movie -- Star Trek Beyond -- was released, producer J.J. Abrams gave a 100% guarantee that a fourth Star Trek movie in the Kelvin Timeline would be made. While not a box office bomb, Beyond did not do gangbusters in the theaters and things got kind of quiet on the new movie front. More recently there was word that director Quentin Tarantino had an idea for a new Trek film, and there was reported movement on that front, though no official announcement.
Though we don't know if it involves the Tarantino film, or the return of George Kirk, it appears that more Star Trek movies are indeed alive. More than alive it seems, as there are two of them in development. At Paramount's presentation during CinemaCom, Paramount CEO Jim Gianopulos said there were several Star Trek movies in the works, which he later clarified to be two. No details were given about the films or any release timeframes, but we now know that Star Trek movies aren't dead, Jim.
Not yet anyway.