On the drink, as a finger is drunk (9)
I believe the answer is:
seafaring
'on the drink' is the definition.
(the drink can mean the sea)
'as a finger is drunk' is the wordplay.
'is drunk' indicates an anagram.
'as'+'a'+'finger'='asafinger'
'asafinger' with letters rearranged gives 'SEAFARING'.
(Other definitions for seafaring that I've seen before include "Sailor's way of life" , "ocean travel" , "Travelling the ocean" , "Travelling by ship" , "So Jack's likely to be" .)