Second unfinished drink (5)
I believe the answer is:
latte
'drink' is the definition.
(type of coffee drink)
'second unfinished' is the wordplay.
'second' becomes 'latter' (latter can mean the second of two mentioned things).
'unfinished' means to remove the last letter.
'latter' with its last letter removed is 'LATTE'.
(Other definitions for latte that I've seen before include "hot drink" , "Style of coffee" , "See 21" , "Frothy milky coffee" , "Kind of espresso coffee" .)