hierarch vs priest

hierarch and priest both are nouns.

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

As nouns, priest is a hypernym of hierarch; that is, priest is a word with a broader meaning than hierarch:

hierarch: a senior clergyman and dignitary
priest: a clergyman in Christian churches who has the authority to perform or administer various religious rites; one of the Holy Orders

hierarch (noun)	priest (noun)
a senior clergyman and dignitary	a clergyman in Christian churches who has the authority to perform or administer various religious rites; one of the Holy Orders
a person who holds a high position in a hierarchy	a person who performs religious duties and ceremonies in a non-Christian religion