Mayor in Barnet has almost beaten Labour (11,4)
I believe the answer is:
erymanthian boar
'labour' is the definition.
(I've seen this before)
'mayor in barnet has almost beaten' is the wordplay.
'almost' means to remove the last letter (almost the whole word is kept).
'beaten' is an anagram indicator (letters beaten up or destroyed).
'mayor'+'in'+'barnet'+'has'='mayorinbarnethas'
'mayorinbarnethas' with its last letter removed is 'mayorinbarnetha'.
'mayorinbarnetha' is an anagram of 'ERYMANTHIAN BOAR'.
(Another definition for erymanthian boar that I've seen is " Labour".)