Unsympathetic country offering unpleasant cure for addiction (4,6)
I believe the answer is:
cold turkey
'unpleasant cure for addiction' is the definition.
'unsympathetic country' is the wordplay.
'unsympathetic' becomes 'cold' (I've seen this before).
'country' becomes 'turkey' (Turkey is an example).
'cold'+'turkey'='COLD TURKEY'
'offering' is the link.
(Other definitions for cold turkey that I've seen before include "(Symptoms of) sudden withdrawal of addictive drug" , "result of stopping drugs" , "taken in the days after Christmas?" , "Cure" , "Quick way to come off horse" .)