Food shop, cold, promises to be tasty (9)
I believe the answer is:
delicious
'tasty' is the definition.
(I've seen this in another clue)
'food shop cold promises' is the wordplay.
'food shop' becomes 'deli' (short for delicatessen).
'cold' becomes 'C' (abbreviation, eg on taps).
'promises' becomes 'IOUs' (promises to pay a debt).
'deli'+'c'+'ious'='DELICIOUS'
'to be' is the link.
(Other definitions for delicious that I've seen before include "See 3" , "Pleasant tasting" , "Luscious, toothsome" , "Delightful; tasty" , "Very pleasant to taste" .)