Finished drink, noting area of common interest (7)
I believe the answer is:
overlap
'area of common interest' is the definition.
(I've seen this in another clue)
'finished drink' is the wordplay.
'finished' becomes 'over' (over can mean finished or ended).
'drink' becomes 'lap' (to lap is to drink up).
'over'+'lap'='OVERLAP'
'noting' is the link.
This may not be correct. It may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for overlap that I've seen before include "Coincide in time or space" , "Extend over and cover a part of" , "Imbricate" , "Flap" , "Partly hide" .)