A Primat is the apparent leader of each Ur-Quan faction. Admittedly there are few references to either the Kohr-Ah and Kzer-Za Primats: a Ur-Quan Kzer-Za mentions the Kohr-Ah Primat when The Captain informs it of the existence of the neo-Dnyarri, and the Yehat apparently refer to the Kzer-Za Primat when describing the post-War fate of Admiral ZEX.
It is known that in the case of the Kzer-Za, each member is designated by a number (as is seen in the captain names) that corresponds to their position within the Kzer-Za power hierarchy—the overall leader being Lord 1. The Kohr-Ah captains are similarly named, which may indicate that they use a similar scheme to indicate rank. Therefore "Primat" may be a general title that can also be used to refer to this (Lord 1 in the Kzer-Za case) supreme faction authority — though Lord 1 is not referred by the Spathi as a Primat.
Interesting to note, the Kzer-Za refer to the Kohr-Ah Primat as "she", suggesting that the creature is of feminine gender, possibly the matriarch of the species assuming that Lord 1 and Death 1 are the patriarchs.