Desire heading off to get a bit of food that isn't expensive (7)
I believe the answer is:
cheapie
'that isn't expensive' is the definition.
(something sold cheaply)
'desire heading off to get a bit of food' is the wordplay.
'desire' becomes 'ache' (ache can mean a passionate desire for something).
'heading off' means to remove the first letter.
'to get' says to put letters next to each other.
'bit of food' becomes 'pie'.
'ache' with its initial letter removed is 'che'.
'che'+'a'+'pie'='CHEAPIE'
(Other definitions for cheapie that I've seen before include "Something inexpensive" , "something economical" , "item knocked down?" .)