Struggle between two parties of right and left (4)
I believe the answer is:
duel
'struggle between two parties' is the definition.
(a fight between two people)
'right and left' is the wordplay.
'right' becomes 'due' (due is a kind of right).
'and' means one lot of letters go next to another.
'left' becomes 'L' (common abbreviation).
'due'+'l'='DUEL'
'of' is the link.
(Other definitions for duel that I've seen before include "Fight between two people over an affair of honour" , "Combat to settle a row" , "shoot-out?" , "Affair of honour (between two men)" , "Arranged fight" .)