Fight for fragment (5)
I believe the answer is:
scrap
This clue is a double definition.
'fight' is the first definition.
(a scrap is a minor fight)
'for fragment' is the second definition.
(scrap is a kind of fragment)
(Other definitions for scrap that I've seen before include "Scuffle" , "Fragment or slangy fight" , "Discarded metal or slang fight" , "Argy-bargy" , "Discard the small fragment" .)