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Star Trek XIV is the planned next Star Trek film, following 2016's Star Trek Beyond. Several different treatments have been developed since Star Trek Beyond. By November 2019, only two different projects remained in active development – one based on an idea by Quentin Tarantino, and another written by Noah Hawley – before they too were "shelved indefinitely" (a industry euphemism for permanently cancelled) in 2020.
Quentin Tarantino film
In December 2017, it was reported that Quentin Tarantino had pitched an idea for a Star Trek film to J.J. Abrams.  Tarantino has said he sees the reboot "as an opportunity to expand on those old stories, rather than change them," though he added it would be challenging giving all of the cast something to do in a film.  It was later announced that the film would be written by Mark L. Smith (of The Revenant fame), based off Tarantino's idea. 
In April 2018, Zachary Quinto commented that he believed that there were at least three scripts in development for the film, with Tarantino's being just one of them.  In the same month, he reiterated that Paramount Pictures wanted to make at least one more Star Trek film, implying that the aforementioned scripts could all be turned into films, but Paramount had to decide on the order.  During the same month, Abrams met with Tarantino to discuss the film.  At CinemaCon 2018, Paramount CEO Jim Gianopulos revealed the studio was working on two new Star Trek films. 
In June 2019, Tarantino confirmed in an interview with Empire that a draft script existed and the next step would be for him to evaluate it. He also stated that his movie would be rated R under the MPAA system. 
Ever since the initial 2017 announcement, little else about the Tarantino project has been forthcoming but on 22 July 2019 Tarantino lifted a tip of the veil in an interview given to MTV's Happy Sad Confused podcast series.  He stated at approximately 20:30 into the interview,
Wanting to tell himself a "Guardian of Forever"-type story, Tarantino additionally stated in the same podcast that he was a huge fan of the Star Trek: The Original Series (the series he was referencing in the above quoted remark), especially of how William Shatner played Captain James T. Kirk, but also how he was "(...)actually intrigued by the JJ Abrams version of it is because I thought Chris Pine did a fantastic job not just playing Capt. Kirk but playing William Shatner's captain – he is William Shatner. He's not just another guy, he's William Shatner's Capt. Kirk. And it's literally, Zachary Quinto is literally Leonard Nimoy's – because they both have the same scene together – he's his Spock. They fucking nail it. They just nail it."  Incidentally, known for his fondness of dropping pop-culture references in his body of work, Tarantino had already dropped two Star Trek references in his 2003 film Kill Bill: Vol. 1, including one to (the original) Khan.
In January 2020, Tarantino told Deadline, in reference to the script:
Aside from the fact that Tarantino's closing remark implied that neither a script nor a story treatment had even been submitted yet by this time, him declining his further involvement with Star Trek also chimed with his earlier remark made to Consequence of Sound on 16 December 2019, where he stated, "I think I'm steering away from Star Trek, but I haven't had an official conversation with those guys yet." Tarantino had in the meantime come to the realization that a Star Trek film was probably not the best way to conclude his projected ten-film making career (the intent much publicized about), deeming it too much of an outlier in his hitherto illustrious body of work, particularly after the success of his ninth film, Once upon a Time...in Hollywood (2019, earning two Academy Awards in 2020), the intended penultimate one. 
By May 2020, Tarantino's Star Trek-project appeared to be definitively off the table, even though no official statement has been issued to the affirmative.  Tarantino himself has in the meantime engaged in the pre-production of his tenth film which he has intimated to become an epilogue of sorts to his realized body of work, without further mentioning Star Trek at all.   
On 6 December 2020 however, it was revealed that a R-rated script had in the meantime been written by Mark L. Smith for Tarantino to direct.  Smith had actually already been confirmed to do so three years earlier. What little was known about the story concerned a gangster story set in 1930s, something of a tie-in to the classic episode "A Piece of the Action", or as Tarantino himself described it, a "Pulp Fiction in space". 
In April 2021, Smith described working with Tarantino on the script for this project: "It was through J.J. Abrams, through Bad Robot. I’ve done a few things with them. And so they always bring me stuff… But Tarantino, he wanted to do this. And so we all gathered in a room and we talked about the ways in. After that, they just called me and said, “Hey, are you up for it? Do you want to go? Quentin wants to hook up.” And I said, “Yeah.” And that was the first day I met Quentin, in the room and he’s reading a scene that he wrote and it was this awesome cool gangster scene, and he’s acting it out and back and forth. I told him, I was so mad I didn’t record it on my phone. It would be so valuable. It was amazing. Then just we started working. I would go hang out at his house one night and we would watch old gangster films. We were there for hours… We were just kicking back watching gangster films, laughing at the bad dialogue, but talking about how it would bleed into what we wanted to do."
In the same podcast interview, Smith said that he gave the film "a ten percent chance that it ever gets made". The proposal was eventually abandoned in favor of the film to be directed by Matt Shakman.
Noah Hawley film
On 19 November 2019, Deadline reported that the aforementioned Noah Hawley was in final talks with Paramount Pictures to write and direct a Star Trek film. It would be produced by J.J. Abrams' Bad Robot Productions and Hawley's 26 Keys Productions.  While Hollywood trades presumed Hawley's film would star the (surviving) cast of Star Trek, Star Trek Into Darkness, and Star Trek Beyond, Hawley commented, "It’s still early days. For me, it’s definitely an a new direction, but it’s still early, in terms of who exactly would be in it or what the characters would be. I don’t think of it as Star Trek 4, to be reductive. This is a new beginning." 
There is more to Hawley's remarks than meets the eye as the Star Trek film and television franchises were "reunified" in December 2019, with the former up for re-evalution after the dismal (box office) performance of Beyond, and which could possibly spell the end of Star Trek set in the alternate reality altogether – hence Hawley's "new direction/beginning" observations. Not only that, but Bad Robot has disassociated itself from Paramount,   meaning that it remains to been seen whether or not further participation, if any, of Bad Robot in the film franchise (now controlled by rival production company Secret Hideout under Alex Kurtzman ) is guaranteed, especially in light of Abrams' dissatisfaction with the franchise over merchandising rights,  and Bad Robot's subsequent formal disassociation from Paramount in September 2019.  If not, then any talks Hawley, or Tarantino for that matter, might have had with Bad Robot became moot as they were talking to the wrong people at the time,  arguably explaining both the declining enthusiasm of the latter, as well as the dismissive remarks Abrams made to Tarantino of the alternate reality he himself had helped create.
As if to underscore Hawley's remarks, Montgomery Scott performer Simon Pegg has stated in December 2019 that he was doubtful that Hawley's film would feature any of the alternate reality cast, as neither he, nor to the best of his knowledge, anyone else of the primary cast had been informed of the project,  which was followed on 9 January 2020 by an interview with Hawley to The Hollywood Reporter in which he himself cast doubt on this as well by stating, "I don't know. But new characters often involve new cast,"  implying in another interview, published on the same date, that talks with Kurtzman had indeed commenced as well.  His statements were made after rumors had already started to circulate in the media earlier that week that his film was no longer under consideration either,   considered "too Trekkie" apparently,  even though conflicting reports to the contrary were still being published as well in the same time period.  
If anything, it exemplified the confusion the Star Trek franchise found itself in pursuant the December 2019 reunification in its search for a renewed direction where rights and licenses are concerned, and its resultant confusing and conflicting communications to the outside world.  
On 19 May 2020 Pegg reiterated on Collider his initial 2019 assessment, furthermore expressing his own doubts of any future Star Trek feature film ever coming to pass, when musing, "Maybe television is a better format for Star Trek. That's where it started, you know."  A report on Trekmovie.com the month previously has indeed indicated that Hawley's project, with no discernible progress made (no script or story treatment had even been written yet by Hawley at the time ), had in the meantime become stuck in limbo as well in the wake of severe financial troubles ViacomCBS found itself in because of both the 2020 COVID-19 pandemic, and the deplorable financial state Paramount owner Viacom was in at the time of the reunification with CBS Corporation to begin with. 
By November 2020, it appeared that Hawley's Star Trek film, like the Tarantino film, was definitively off the table as well. In a 29 November 2020 interview to Deadline Hawley responded to a question about the status of the film, "It doesn’t appear to be in my immediate future. I think when Emma came in, she took a look at the franchise and wanted to go in a different direction with it. But you know, life is long, we were very close to production but in this business that doesn’t mean much. You got to get out of the gate to be in the race if you know what I mean."  The "Emma" Hawley referred to concerned Emma Watts, a Paramount executive, who was appointed by National Amusements (owner of ViacomCBS) head Shari Redstone to appraise the status of the Star Trek live-action franchise, both film as well as television, for its (commercial) viability.  Hawley's words were in essence Hollywood-speak for the definitive cancellation of his Star Trek film.
It turned out in June 2021 that Hawley was actually close to start production in Australia (which strongly implied that Hawley had actually finished a shooting script), with the casting process set to begin, when Watts pulled the plug on his film.  As to Watts' "different direction", nothing, save some vague rumors which include the two mentioned hereafter, has been made public, making it appear that the entire film franchise too is terminated for the time being.
Star Trek: Discovery film
In an interview with the podcast Things are Going Great for Me, Chris Pine indicated that there was/is some sort of film about Star Trek: Discovery planned: "Tarantino is going to do one. And then, who is it? Noah Hawley was going to do something else, and then that fell through. And then he’s going to do something with the Discovery, the new Alex Kurtzman-led cast." 
Kalinda Vazquez film
On 4 March 2021, it was reported that Star Trek: Discovery writer, Kalinda Vazquez was hired by Paramount and J.J. Abrams to write a script for "an original movie".  This was reputedly not the film the studio had announced for a June 2023 release, but a different project altogether. 
Matt Shakman film
Star Trek Beyond
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Not yet announced