A piece of processed American cheese (4)
I believe the answer is:
edam
'cheese' is the definition.
(I know that Edam is a type of cheese)
'a piece of processed american' is the wordplay.
'a piece of' indicates a hidden word.
'EDAM' can be found hidden inside 'processed american'.
(Other definitions for edam that I've seen before include "Sphere of Dutch cheese" , "Danish cheese" , "Kind of cheese" , "Yellow cheese with a red covering" , "Madeinto popular cheese" .)