Stay - there's a little drink left (7)
I believe the answer is:
support
'stay' is the definition.
(I've seen this before)
'a little drink left' is the wordplay.
'a little drink' becomes 'sup' (sup can mean a small drink).
'left' becomes 'port' (left side of a ship - opposite of starboard).
'sup'+'port'='SUPPORT'
'there's' acts as a link.
(Other definitions for support that I've seen before include "Prop" , "Cheer" , "used to give strength?" , "Keep from falling, as crutch does (7)" , "Give assistance to" .)