Finished with a type of food (5)
I believe the answer is:
pasta
'type of food' is the definition.
'finished with a' is the wordplay.
'finished with' becomes 'past' (past can mean forgotten or finished).
'past'+'a'='PASTA'
(Other definitions for pasta that I've seen before include "Fusilli, tortelloni etc" , "Dried flour paste, staple in Italian food" , "Penne, rigatoni etc" , "shells, perhaps" , "Tapas (anag)" .)