Second unfinished coffee (5)
I believe the answer is:
latte
'coffee' 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 taken off is 'LATTE'.
(Other definitions for latte that I've seen before include "hot drink" , "Espresso added to frothed steamed milk" , "Italian word for milk" , "Coffee with a topping of frothed steamed milk" , "frothy cup" .)