Fantastic avenger giving chase (7)
I believe the answer is:
engrave
'chase' is the definition.
(I've seen this before)
'fantastic avenger' is the wordplay.
'fantastic' is an anagram indicator.
'avenger' anagrammed gives 'ENGRAVE'.
'giving' acts as a link.
(Other definitions for engrave that I've seen before include "Cut or carve (a text)" , "Cut (design) into a hard surface" , "Carve into metal" , "Carve into surface as of medal" , "Fix" .)