Yesterday's Enterprise: Tarantino's Other Pick
Interestingly, the other episode mentioned by Tarantino in the podcast is "Yesterday's Enterprise," which is a thematic cousin to "The City on the Edge of Forever."
In the episode, a temporal anomaly transports the Enterprise-C twenty-two years into the future, changing history. In the altered present, the Federation of Captain Picard (Captain of the Enterprise-D) is at war with the Klingon Empire; the Enterprise-C was supposed to be destroyed protecting a Klingon outpost from hostile Romulan forces. This act of selfless compassion and fighting honorably against insurmountable odds serves as a diplomatic cornerstone which helps to maintain the tentative peace that had been established in Star Trek VI. Without the sacrifice of the Enterprise-C, a war broke out which took the lives of forty billion people in the altered timeline.
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Tarantino praised the episode for "the way it dealt with the mythology" of Star Trek. The only person who realizes that history has been changed is Guinan, played by Whoopi Goldberg, who is able to sense disruptions in the timeline. She must convince this alternate, war-weary version of Picard that the only way to set history right is to doom the Enterprise-C to certain death in the past.
The episode is considered one of the best of The Next Generation, but it seems unlikely that Paramount would want to ditch the rebooted Original Series universe and jump into the era of TNG. Instead, maybe the episode could return to where it all began and feature the USS Kelvin transported into the alternate timeline of the J.J. Abrams movies. Back when the next entry in the new film series was first being developed (in the lead-up to the launch of Star Trek Beyond), it was rumored that Chris Hemsworth would return to play George Kirk, the doomed first officer of the Kelvin. George's death at the hands of the time-traveling Romulan, Nero, created the alternate timeline in which the rebooted films are set.
In 2009's Star Trek, Spock travels back in time along with Nero and gets stranded in the alternate universe which the fans call the "Kelvin Timeline." What if Tarantino's movie takes that theme and crosses it with that of "Yesterday's Enterprise," of setting right what had gone wrong; what if the rebooted Enterprise goes back in time to rescue the Kelvin, ensuring that the Prime timeline plays out the way it's supposed to, but at the cost of stranding the future Enterprise in a universe to which it doesn't belong?
Chris Pine's version of Kirk will have saved his father and preserved the original timeline, but he'd be unable to return to the only universe he ever knew. That is, of course, unless they found a way to travel across dimensions, like the distortion to the Mirror Universe shown in "The Tholian Web" and its Star Trek: Enterprise crossover, "In a Mirror, Darkly." Perhaps Whoopi Goldberg could appear in the film as Guinan, aware that she's in an alternate universe, and conflicted as to whether the Kelvin timeline should be allowed to exist as a separate reality, or if it's an aberration to the timeline which must be corrected.
It wouldn't be a direct adaptation of the TNG story, granted, but it would be true to the spirit of the episode, of dutiful sacrifice in service of the greater good, while bringing the Kelvin Timeline full-circle. Plus, it wouldn't necessarily preclude the possibility of the Chris Pine/Zachary Quinto versions of the crew from having further adventures in the restored Prime universe.
Of course, maybe Quentin Tarantino's plan for a new Star Trek movie is completely different from what he had mused on with The Nerdist two years ago. Maybe he's thinking of adapting a completely different episode; or maybe he has a whole new idea for where to take the franchise which isn't based on a preexisting Trek story. It's also entirely possible he might not be interested in using the established cast of the J.J. Abrams movies, even though Abrams is still developing the film as a producer. Pine, Quinto, and the rest are presumably contracted to appear if called upon, but it's unclear whether or not Tarantino even has them in mind for whatever his version of Trek may entail.
Whatever the case may be, here's hoping that aramount lets Quentin run wild and gives him the creative freedom he needs and deserves to implement his vision for Star Trek.