Left after outstanding fight (4)
I believe the answer is:
duel
'fight' is the definition.
(duel is a kind of fight)
'left after outstanding' is the wordplay.
'left' becomes 'l' (common abbreviation).
'after' means one lot of letters go next to another.
'outstanding' becomes 'due' (I've seen this before).
'l' after 'due' is 'DUEL'.
(Other definitions for duel that I've seen before include "Gentlemen's disagreement" , "battle" , "Prearranged fight with deadly weapons between two people" , "Combat to settle a row" , "Arranged fight" .)