Party leader in Brighton meeting Prime Minister, briefly, for fight (2,6)
I believe the answer is:
do battle
'fight' is the definition.
(to do battle is to fight)
'party leader in brighton meeting prime minister briefly' is the wordplay.
'party' becomes 'do' (do can informally mean a party).
'leader in' indicates taking the first letters.
'meeting' says to put letters next to each other.
'prime minister briefly' becomes 'attle' (I am not sure about this - if you are sure you should believe this answer much more).
The initial letter of 'brighton' is 'b'.
'do'+'b'+'attle'='DO BATTLE'
'for' is the link.
Can you help me to learn more?
(Another definition for do battle that I've seen is " Fight".)