The hand to hand combat prowess of STNG Starfleet's security personnel is lauded by Tasha Yar in the accepted answer to this question.
Tasha: I think you should know that there is no physical training anywhere that matches Starfleet, especially its security people.
It is likely combat training evolved during the time elapsed between TOS and STNG, but Kirk definitely had specific moves which he seemed to be trained in and repeatedly used during his 5 year mission.
While some of the moves are identifiable, I find it difficult to pin a label on the double handed, flying hip check, style William Shatner utilized in his portrayal of James Kirk. According to canon, is Kirk practicing a known fighting style, and if so, what is it?