According the the best available info (TOS: Day of the Dove) the crew complement of a typical D-7 Klingon Cruiser is four hundred(ish).
KIRK: Maintain Red Alert.
(The Klingons arrive, and their leader hits Kirk with his disruptor,
knocking him down.)
KANG: You attacked my ship! Four hundred of my crew dead. Kirk, my ship is disabled. I claim yours. You are now prisoners of the
Klingon Empire against which you have committed a wanton act of war!
At this point we're stuck with informed guesswork.
Since we know (courtesy of Star Trek III) that the complement of the slightly smaller TOS-Era Bird of Prey is only "about a dozen officers and men", it stands to reason that the remainder of crew of the D-7 (some 350 extra personnel) are likely to be a mixture of boarding parties and security officers.