Cream were first to get drunk (7)
I believe the answer is:
pickled
'drunk' is the definition.
(thesaurus)
'cream were first' is the wordplay.
'cream' becomes 'pick' ('pick' can be a synonym of 'cream').
'were first' becomes 'led'.
'pick'+'led'='PICKLED'
'to get' is the link.
(Other definitions for pickled that I've seen before include "Blotto" , "Preserved in vinegar or brine" , "Soused" , "Preserved in liquid" , "Preserved - drunk" .)