New Avenger giving chase (7)
I believe the answer is:
engrave
'chase' is the definition.
(I've seen this before)
'new avenger' is the wordplay.
'new' indicates anagramming the letters.
'avenger' with letters rearranged gives 'ENGRAVE'.
'giving' acts as a link.
(Other definitions for engrave that I've seen before include "Etch" , "impress deeply" , "Mistakes" , "Incise" , "Carve into surface as of medal" .)