Fight for the left-overs (5)
I believe the answer is:
scrap
'fight' is the definition.
(a scrap is a minor fight)
I don't understand how the rest of the clue works.
Can you help me to learn more?
(Other definitions for scrap that I've seen before include "Get rid of" , "Waste metal or slang fight" , "Tiny piece; abolish" , "Small piece; abolish" , "Quarrel" .)