quest after vs seek

quest after is not a noun while seek is a noun.

Word	Noun	Adjective	Verb	Adverb
quest after	No	No	Yes	No
seek	Yes	No	Yes	No

As verbs, seek is a hypernym of quest after; that is, seek is a word with a broader meaning than quest after:

Other hypernyms of quest after include look for, search.

quest after (noun)	seek (noun)
	the movement of a read/write head to a specific data track on a disk

quest after (verb)	seek (verb)
go in search of or hunt for	inquire for
	try to locate or discover, or try to establish the existence of
	go to or towards
	try to get or reach
	make an effort or attempt