Fight for a little bit (5)
I believe the answer is:
scrap
This clue is a triple definition!
'fight' is the first definition.
(a scrap is a minor fight)
'for' is a link.
'a little' is the second definition.
(thesaurus)
'bit' is the third definition.
(I know that bit can be written as scrap)
(Other definitions for scrap that I've seen before include "Fragment or slangy fight" , "Tussle over junk metal?" , "Ditch - dust-up" , "Discarded metal or slang fight" , "bundle" .)