Second drink from anonymous person? (7)
I believe the answer is:
another
I believe this is a double definition.
'second drink' is the first definition.
'anonymous person?' is the second definition.
(A.N. Other can mean an unspecified person)
'from' is the link.
(Other definitions for another that I've seen before include "A further (item)" , "Somebody else" , "encore?" , "Player or person not yet named or selected" , "A different one" .)