Party hearing about delivery groups likely to provoke argument (13)
I believe the answer is:
controversial
'likely to provoke argument' is the definition.
(something controversial causes arguments)
'party hearing about delivery groups' is the wordplay.
'party' becomes 'con' (abbreviation for Conservative Party).
'hearing' becomes 'trial' (I've seen this before).
'about' is an insertion indicator.
'delivery groups' becomes 'overs' (cricket - groups of six deliveries).
'trial' going around 'overs' is 'troversial'.
'con'+'troversial'='CONTROVERSIAL'
(Other definitions for controversial that I've seen before include "At issue" , "Causing heated debate" , "Tendentious" , "Debatable, likely to arouse dispute" , "Likely to cause disagreement" .)