here's an idea: what about a villain that's not a one-shot character? Like either a background recurring villain who's not the center of the story or a main villain that lasts for a few movies, like Darth Vader in Star Wars, who gets defeated in ANH but escapes to be in the next two.
How about Captain Garth? Maybe we could see the events that made him lose his mind, and see him in command of a starship run like a pirate ship. You know, half his crew supports him and the other half...tough luck.
Only leave out all that "cellular metamorphosis" stuff.
I think Garth would make a good recurring nemesis for Kirk. He's a superior, more experienced commander, but because he's insane he wouldn't be held back by all those pesky Starfleet regulations.
Oh, and give him a cool ship.