The next people would hear of Star Trek 4 was that Paramount had quietly canceled the movie.
The film likely has a smaller budget than Star Trek and no overlapping cast.
It’s unknown how this affects Tarantino’s project, but one would imagine that it’s still happening pending the director’s schedule/interest.
Paramount hasn’t confirmed the news, but without two of the most important cast members and a director, it makes sense that Star Trek 4 was sent out to pasture, though it’s unclear if the studio will attempt to pick up the torch again in the future.