chase after vs hound

chase after is not a noun while hound is a noun.

Word	Noun	Adjective	Verb	Adverb
chase after	No	No	Yes	No
hound	Yes	No	Yes	No

As verbs, hound is a hyponym of chase after; that is, hound is a word with a more specific, narrower meaning than chase after:

Other hyponyms of chase after include tree, quest, hunt, trace, run down.

chase after (noun)	hound (noun)
	any of several breeds of dog used for hunting typically having large drooping ears
	someone who is morally reprehensible

chase after (verb)	hound (verb)
go after with the intent to catch	pursue or chase relentlessly
pursue someone sexually or romantically