Talking to Slashfilm, Tarantino said that his boarding that particular franchise is "a very big possibility. I haven’t been dealing with those guys for a while cause I’ve been making my movie. But we’ve talked about a story and a script. The script has been written and when I emerge my head like Punxsutawney Phil, post-'Once Upon a Time in Hollywood,' we’ll pick up talking about it again."
QT reportedly first pitched his R-rated "Star Trek" to Paramount in 2017. If Tarantino does decide to boldly go into the Trekverse, it's likely he'd need a whole new cast.
After three feature films, beginning with J. J. Abram's 2009 reboot, a fourth film with that lineup is looking less and less likely. Chris Pine said he's still game to play Captain Kirk, even though negotiations over money have gotten nowhere.