Long-running quarrel (4)
I believe the answer is:
feud
'long-running quarrel' is the definition.
(I've seen this before)
This is all the clue.
(Other definitions for feud that I've seen before include "Long-running dispute" , "Long-running quarrel" , "Private war" , "State of prolonged mutual hostility" , "Prolonged fight between families, very Sicilian" .)