quest vs ask for

quest is a noun but ask for is not a noun.

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

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

Other synonyms of quest include bespeak, call for, request.

quest (noun)	ask for (noun)
the act of searching for something
a search for an alternative that meets cognitive criteria

quest (verb)	ask for (verb)
seek alms, as for religious purposes	express the need or desire for
express the need or desire for	increase the likelihood of
bark with prolonged noises, of dogs
search the trail of (game)
make a search (for)