Partly cover remaining drink (7)
I believe the answer is:
overlap
'partly cover' is the definition.
(I've seen this before)
'remaining drink' is the wordplay.
'remaining' becomes 'over' (as in 'we ate them all but had one over').
'drink' becomes 'lap' (to lap is to drink up).
'over'+'lap'='OVERLAP'
(Other definitions for overlap that I've seen before include "have something in common" , "Ride" , "Extend on top of" , "Coincide in part" , "Partially coincide" .)