quest after vs quest for

quest after and quest for both are verbs.

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

As verbs, quest after and quest for are synonyms defined as:

Other synonyms of quest after include go after, pursue.

quest after (verb)	quest for (verb)
go in search of or hunt for	go in search of or hunt for