chase vs chase after

chase is a noun but chase after is not a noun.

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

As verbs, chase and chase after are synonyms defined as:

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

As verbs, chase and chase after are synonyms defined as:

chase (noun)	chase after (noun)
the act of pursuing in an effort to overtake or capture
a rectangular metal frame used in letterpress printing to hold together the pages or columns of composed type that are printed at one time

chase (verb)	chase after (verb)
cut a groove into	go after with the intent to catch
cut a furrow into a columns	pursue someone sexually or romantically
go after with the intent to catch
pursue someone sexually or romantically