Warning: SPOILERS for Star Trek: Discovery season 3 finale.
Michael Burnham (Sonequa Martin-Green) became a Captain in Star Trek 2009. Not surprisingly, Alex Kurtzman co-wrote the movies Abrams directed and he's also the executive producer of Star Trek: Discovery. Burnham's whirlwind course to commanding Discovery comes right out of Kirk's Star Trek 2009 movie playbook.
In Star Trek, Kirk was a cadet who stowed away aboard the Starship Enterprise commanded by Captain Christopher Pike (Bruce Greenwood), who initially sponsored Jim's enlistment into Starfleet and tempted him with his destiny to be greater than his father, Lt. George Kirk (Chris Hemsworth). During the course of the film, which mostly happened over a couple of days tops, Kirk improbably jumped from Cadet to First Officer to being thrown off the ship by Spock (Zachary Quinto) to becoming Acting Captain of the Enterprise as he battled and ultimately defeated the villainous Romulan time-traveler Nero (Eric Bana). When the crisis was over and Earth was saved, Kirk received a promotion to Captain and was given command of the Enterprise by Pike and Starfleet. It was, essentially, the career of William Shatner's Prime universe version of Kirk condensed into a blisteringly fast two hours.
In Star Trek: Discovery's season 3 finale, "That Hope Is You, Part 2", Michael went from being a prisoner of Osyraa (Janet Kidder), the leader of the Emerald Chain, to commanding Discovery as Acting Captain in the absence of Captain of Discovery, Saru, to step aside so she could become Captain and assume command, just as Kirk relieved Pike of his command at the conclusion of Star Trek.
Michael's checkered Starfleet career curtailed her original trajectory towards the Captain's chair but the seeds for Burnham's newfound promotion were planted earlier in Star Trek: Discovery season 3. Burnham questioned her future in Starfleet just as Kirk did at the start of Star Trek 2009, and Emperor Philippa Georgiou (Michelle Yeoh) flat out told Michael she deserved to be Captain, similar to how Pike challenged Kirk to be greater than his father. After they learned of the Kelpien, Su'Kal (Bill Irwin), who was stranded in the Verubin Nebula, Burnham openly questioned whether Captain Saru was too emotionally compromised to command Discovery, which is the exact same logic Kirk used to take the Enterprise from Spock after the Vulcan was distraught from the annihilation of his homeworld and people.
As if the Kirk allusion wasn't clear enough, "That Hope Is You, Part 2" even had a direct reference to one of the Enterprise Captain's most famous acts when Zareh (Jake Webber) told Burnham that she was in "a no-win situation" and Michael responded, "Oh, I don't believe in those." Not believing in the no-win scenario is a hallmark of Kirk, who cheated to beat Starfleet Academy's Kobayashi Maru test in both the Prime and Kelvin timelines. In her own way, Burnham outfoxed Osyraa and beat her so-called no-win situation by taking insane risks that paid off. And, as Shatner's Kirk famously espoused in Star Trek: The Original Series, "Risk is our business!" iral Vance (Oded Fehr) even applauded Burnham's risk-taking ways, which he itted "worked", when he asked Michael to Captain Discovery.
Star Trek: Discovery has scored greatly from Burnham being Spock's adopted sister and exploring the similarities between them. Meanwhile, unlike Spock, Kirk seems to be a forgotten man with no apparent legacy to speak of in Star Trek's 32nd-century future. But by mimicking Kirk's heroic rise to command in Star Trek 2009, "That Hope Is You, Part 2" essentially transformed Captain Michael Burnham into the new version of Captain Kirk, and Discovery's season 3 finale brings the point home by playing the classic Alexander Courage TOS theme music over its credits just like Star Trek 2009 did. More so, Michael is now a hybrid; a highly-intelligent yet incomparably-daring fusion of the best aspects of Kirk and Spock as she Captains her starship going into Star Trek: Discovery season 4.