Seeking office, British PM loses European conflict (7,6)
I believe the answer is:
running battle
'conflict' is the definition.
(an ongoing confrontation or conflict)
'seeking office british pm loses european' is the wordplay.
'seeking office' becomes 'running' (running for public office).
'british' becomes 'b' (abbreviation e.g. in 'BBC').
'pm' becomes 'attlee' (Clement Attlee).
'loses' is a deletion indicator.
'european' becomes 'E' (abbreviation e.g. EU).
'attlee' with 'e' removed is 'attle'.
'running'+'b'+'attle'='RUNNING BATTLE'
(Other definitions for running battle that I've seen before include "Continuing skirmish" , "Fight carrying on continuously" , "drawn-out dispute" , "Moving engagement" , "Military engagement whilst on the move" .)