This is AOS Kirk/Spock Prime.
Poor AOS Kirk never had a father, and the attention, affection, and approval of an older man have been all too rare in his life ... which makes him gravitate towards Spock Prime and makes him blossom under his affection like a flower in the sun.
Kirk is kind of wild and knows he's kind of wild, but he's always been able to think rings around everyone else, so he can get away with stuff pretty much everywhere. Plus, he's never really respected anyone enough to let them tame him. But he can't think rings around Spock Prime, who is at least as smart as Kirk is AND has a lot of experience with another Kirk AND has Vulcan mental powers.
Like a lot of powerful men, Kirk has a previously unrealized desire for a D/S relationship, with himself as the submissive. He may or may not realize that he's even more inclined this way than most powerful men, because he never had the loving guidance of a father.
He'd thought he would never be able to find anyone who was capable of controlling him or who he'd respect and trust enough to allow it. But even old Vulcans are a lot stronger than humans, plus Spock Prime's mental powers have strengthened throughout his life, making him a really awesome telepath at this point in his life, even stronger than young Spock. And Kirk trusts him as he trusts no one else, because he's been in Spock Prime's mind, and he's seen how much Spock Prime loves any and all men named Jim Kirk. So Spock Prime could control Kirk physically, mentally, every way there is -- he has both the ability AND Kirk's trust and respect -- so he's probably the only one that Kirk could ever allow himself to play this sort of game with.
Spock Prime is too ethical to actually DO this until Kirk reveals that he needs and wants it, at which point Spock Prime reveals that he's been holding back on account of not wanting to do anything Kirk doesn't desire, but being Kirk's very physical dom is actually better for him (closer to the usual Vulcan style, maybe?) than the human-style vanilla sex they've been having.
Please, although Kirk is especially susceptible to this sort of relationship because of not having had a father, please do NOT have him call Spock Prime "Daddy."
Kirk is still captain of the Enterprise, but he sees Spock Prime very regularly, on the order of every three or four weeks. Maybe the Enterprise is sent to New Vulcan once a month for whatever reason appeals to you, maybe Spock Prime is doing some sort of special project for Starfleet that requires him to interface with the Enterprise's crew once a month or so. (Depending on your own personal tastes, Kirk may or may not have standing "assignments" from Spock Prime to continue this aspect of their relationship while they're apart.) But Spock Prime isn't stationed ON the Enterprise, because Kirk will need some time apart from Spock Prime's influence, for the following reason:
Unbeknownst to Kirk in the beginning, Spock Prime is not just dominating Kirk for fun and games. He sees the ways in which Kirk's youth and his lack of a father have made him less suited to the captain's role than Kirk Prime was, and the domination that Spock Prime does is actually a series of lessons, teaching Kirk patience and self-control and actually THINKING before acting, and all those good things. Spock Prime knows and appreciates what Kirk has to offer as Kirk -- he's not trying to turn Kirk into a Vulcan -- but he IS trying to turn AOS Kirk into the mature, seasoned, thoughtful man that TOS Kirk was.
Only after they've been doing this for quite awhile does Kirk catch on to the fact that every time he comes back from a session with Spock Prime, he's a more effective captain. He thinks about missions they've had and how his new self-control made the most recent mission work, whereas it would have failed if he'd not had it. And in the mission before that, he needed the patience that Spock Prime had taught him to succeed in that one, or it would have failed, too, without what Spock Prime was teaching him.
Kirk isn't mad about this -- he loves, loves, loves being a great captain -- but he does confront Spock Prime about it, in a mostly admiring kind of way. Kind of an "I'm on to you, you sneaky Vulcan, and you've been training me to be a better captain, haven't you? Are you SURE you're getting something out of our sessions? You aren't closing your eyes and thinking of Starfleet, are you?" Spock Prime will, of course, say that getting to love Kirk was more than he'd ever hoped to have, and getting to train him is so very hot that he would be getting too much out of their sessions unless he were also improving Kirk into the bargain.
Young Spock is romantically happy with Uhura but is very close friends with Kirk. He is surprised at first that Kirk is in love with Spock Prime, and if you want, he and Spock Prime can have a conversation where Spock Prime explains how the features of AOS Kirk's personality make him especially desirous of a relationship with an older man who trains him with both affection and strictness. After that, young Spock is very supportive of Kirk's relationship with Spock Prime. He's glad that they're making each other happy, and he's smart enough to observe that whatever Spock Prime is doing is making Kirk an even better captain than he already was, AND he's smart enough not to mention this to Kirk until the captain catches on by himself, for fear of undermining whatever it is that's making Kirk even better.
Spock Prime uses some pretty intense D/S to train Kirk, with a lot of rough physical stuff that Kirk gets off on -- adrenaline junkie and masochistic starter-of-bar-fights that he is -- but he never uses humiliation. He adores Kirk and treats him like a treasure; even when he's doing D/S with Kirk, Kirk is a greatly valued possession. But although he can pamper Kirk like crazy after a scene, he IS rough with him. Kirk is a brave, strong, and resilient person, and enough to wake up HIS adrenaline and make HIM feel alive is more than most people could handle. But Spock Prime understands Kirks in general very well, plus he has the telepathic advantage. So he always knows exactly how much Kirk needs to bring him to where they both want him to go.
This is probably best set after Star Trek but before Into Darkness. Kirk's death in Into Darkness might make either Spock Prime or Kirk himself a little less enthusiastic about rough physical stuff, and Kirk is a more seasoned and less impulsive man in Beyond, so he wouldn't need this as much then. (And of course Spock Prime dies in Beyond, but I'm firmly pretending that never happened.) But it's up to you; if you can make it work set after Beyond, that's fine with me!
Bonus points for rough sex, spanking, biting, scratching, flogging, fairly serious BDSM
and not just a few playful swats, mind melds, and Vulcan mental control over physiological processes (either Spock Prime's own physiological processes, or control over Kirk's via meld).