Georgiou & Kirk
Out of all the Star Trek captains, I think Georgiou and Kirk are not only one of the duos who are most similar to each other, but also one of the duos who would work best together should the opportunity arise. (For example, Janeway and Sisko, Freeman and Picard, or Pike and Janeway could all also be compared as relatively similar to each other, but would any of those duos work well together? Maybe Freeman and Picard on a good day, but as for the others…hm.)
As this post points out, Georgiou’s [“What will you do if we’re trapped here for eighty-nine years?”] “That’s easy, I’d escape” line has an extremely Kirk energy. The two of them share a take-a-third-option ethos and a mischievous sense of resourcefulness, and for both of them, this is implied to come from a place of past trauma. Kirk survived the massacre at Tarsus IV, where Kodos called it “necessary” to kill many people to “solve” a crisis; at the Academy, he hacked the Kobayashi Maru out of a refusal to accept being told “sometimes losses are inevitable.” For her part, Georgiou had “seen a life of loss, but still chose hope.” She is someone who has experienced enough personal tragedy that she herself, despite her generally upbeat personality, bluntly characterizes her own whole life as being “a life of loss.” But she chooses to find hope in her commitment to and love for the people and universe around her. Kirk and Georgiou are both people forged in tragedy who have made it their ethos to refuse to allow the propagation of tragedy. And, of course, they’re also both people who, when push comes to shove and they are faced with unwinnable scenarios, choose to risk themselves before others.
When it comes to the two of them meeting, we can talk either within the timeline, with Georgiou as an older, experienced officer while Kirk is at the Academy and beginning his career, or via time travel, for a scenario where TOS-era Kirk meets DSC-era Georgiou in classic crossover fashion.
Of course, a post about the within-the-timeline option is not complete without mention of the time the two of them do meet in novel canon. In the Lorca and Georgiou DSC prequel novel Drastic Measures, fortysomething then-Commander Georgiou leads the team of Starfleet and civilians responding to the famine at Tarsus IV, arriving not long after the massacre, while then-Commander Lorca is stationed at a Tarsus IV Starfleet outpost; Georgiou briefly meets Winona and early-teens Jim Kirk during her time there.