Former area supplying Italian food (5)
I believe the answer is:
pasta
'italian food' is the definition.
(type of Italian food)
'former area' is the wordplay.
'former' becomes 'past' (similar in meaning).
'area' becomes 'a' (maths abbreviation).
'past'+'a'='PASTA'
'supplying' acts as a link.
(Other definitions for pasta that I've seen before include "shells, perhaps" , "Fare from Italy" , "dish high in carbohydrates" , "Linguine, e.g." , "Flour and water foodstuff" .)