In spring, a redhead could be fighting (8)
I believe the answer is:
sparring
'be fighting' is the definition.
(to spar is to box)
'in spring a redhead' is the wordplay.
'in' is an insertion indicator.
'redhead' becomes 'r' (the head/first letter of 'red').
'a'+'r'='ar'
'spring' placed around 'ar' is 'SPARRING'.
'could' is the link.
(Other definitions for sparring that I've seen before include "practising for the fight" , "Boxing" .)