go after vs quest after

go after and quest after both are verbs.

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

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

Other synonyms of go after include pursue, quest for.

go after (verb)	quest after (verb)
go in search of or hunt for	go in search of or hunt for
go after with the intent to catch