primate vs hierarch

primate and hierarch both are nouns.

Word	Noun	Adjective	Verb	Adverb
primate	Yes	No	No	No
hierarch	Yes	No	No	No

As nouns, primate and hierarch are synonyms defined as:

Other synonyms of primate include archpriest, high priest, prelate.

primate (noun)	hierarch (noun)
any placental mammal of the order Primates; has good eyesight and flexible hands and feet	a senior clergyman and dignitary
a senior clergyman and dignitary	a person who holds a high position in a hierarchy