Finished drink, partly a coincidence (7)
I believe the answer is:
overlap
'partly a coincidence' is the definition.
(two things which coincide might overlap)
'finished drink' is the wordplay.
'finished' becomes 'over' (similar in meaning).
'drink' becomes 'lap' (to lap is to drink up).
'over'+'lap'='OVERLAP'
(Other definitions for overlap that I've seen before include "Partly coincide in time, area etc" , "bit of a coincidence" , "Partially coincide" , "as do the signs you can see in libraries" , "Project" .)