Bird having fight after fight, aggressive type (11)
I believe the answer is:
sparrowhawk
'bird' is the definition.
(I've seen this before)
'fight after fight aggressive type' is the wordplay.
'fight' becomes 'spar' (sparring is a kind of fighting).
'after' is a charade indicator (letters next to each other).
'fight' becomes 'row' (I've seen this in another clue).
'aggressive type' becomes 'hawk' (I've seen this in another clue).
'spar'+'row'+'hawk'='SPARROWHAWK'
'having' is the link.
(Other definitions for sparrowhawk that I've seen before include "It predates" , "Bird of prey" .)