The fight for proper money (4)
I believe the answer is:
duel
'the fight' is the definition.
(duel is a kind of fight)
'proper money' is the wordplay.
'proper' becomes 'due' (I've seen this before).
'money' becomes 'l' (L can mean 'pounds').
'due'+'l'='DUEL'
'for' acts as a link.
(Other definitions for duel that I've seen before include "Two-person combat" , "shoot-out?" , "Gentlemen's disagreement" , "Potentially fatal fight between two people" , "Contest to settle point of honour" .)