Fight for a bit (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 bit' is the second definition.
(synonyms)

(Other definitions for scrap that I've seen before include "Fight - morsel" , "Get rid of" , "Fragment or morsel" , "Small (leftover) piece" , "Just a fragment, maybe of food" .)

I've seen this clue in The Irish Independent, The Globe and Mail and The Times.

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