(covers information from several alternate timelines)
Hand-to-hand combat, or close quarters combat, refers to various forms of martial arts based upon physical contact between two opponents, usually both trying to harm or subdue the other.
In 2258 of the alternate reality, Christopher Pike asked for any officer trained in advanced hand-to-hand combat to dive to the surface of Vulcan in an attempt to stop Narada from drilling into the planet's surface. Hikaru Sulu volunteered, and James Kirk and Engineer Olson accompanied him. (Star Trek)
In 2269, Captain James Kirk fought Garth in his (Kirk's) form in a hand-to-hand struggle while Spock, unable to tell them apart, waited to see who emerged victorious before intervening. (TOS: "Whom Gods Destroy")