The fight by a mug to take credit (5)
I believe the answer is:
scrap
'the fight' is the definition.
(I've seen this before)
'a mug to take credit' is the wordplay.
'a mug' becomes 'sap'.
'to take' indicates putting letters inside.
'credit' becomes 'cr'.
'sap' enclosing 'cr' is 'SCRAP'.
'by' acts as a link.
(Other definitions for scrap that I've seen before include "Waste metal or slang fight" , "boxing match?" , "Fragment or remnant" , "Discard the small fragment" , "Oddment" .)