give chase vs trail

give chase is not a noun while trail is a noun.

Word	Noun	Adjective	Verb	Adverb
give chase	No	No	Yes	No
trail	Yes	No	Yes	No

As verbs, give chase and trail are synonyms defined as:

Other synonyms of give chase include chase, chase after, dog, go after, tag, tail, track.

give chase (noun)	trail (noun)
	a path or track roughly blazed through wild or hilly country
	evidence pointing to a possible solution
	a track or mark left by something that has passed

give chase (verb)	trail (verb)
go after with the intent to catch	drag loosely along a surface; allow to sweep the ground
	hang down so as to drag along the ground
	go after with the intent to catch
	move, proceed, or walk draggingly or slowly
	to lag or linger behind