A gin Alec's drunk as a painkiller (9)
I believe the answer is:
analgesic
'a painkiller' is the definition.
('analgesic' can be a synonym of 'painkiller')
'a gin alec's drunk' is the wordplay.
'drunk' is an anagram indicator.
'gin'+'alecs'='ginalecs'
'ginalecs' is an anagram of 'nalgesic'.
'a'+'nalgesic'='ANALGESIC'
'as' is the link.
(Other definitions for analgesic that I've seen before include "Anodyne" , "Acting to relieve pain" , "result is soothing" , "Pain-killer" , "Relieving pain" .)