primate (n.)
"high bishop," c.1200, from Old French primat and directly from Medieval Latin primatem (nominative primas) "church primate," noun use of Late Latin adjective primas "of the first rank, chief, principal," from primus "first" (see prime (adj.)).

Meaning "animal of the biological order including monkeys and humans" is attested from 1876, from Modern Latin Primates (Linnæus), from plural of Latin primas; so called from supposedly being the "highest" order of mammals (originally also including bats).