Fight for a piece (5)
I believe the answer is:
scrap
I believe this is a double definition.
'fight' is the first definition.
(a scrap is a minor fight)
'for a piece' is the second definition.
(scrap is a kind of piece)
(Other definitions for scrap that I've seen before include "Tiny piece; abolish" , "Fight; abolish" , "Discarded metal or slang fight" , "Axe" , "Small fight about a smal fragment" .)