The dog, dear, doesn’t have a dish (7)
I believe the answer is:
chowder
'dish' is the definition.
(chowder is a kind of dish)
'the dog dear doesn't have a' is the wordplay.
'the dog' becomes 'chow' (chow is a kind of dog**).
'doesn't have' suggests deleting specific letters.
'dear' with 'a' removed is 'der'.
'chow'+'der'='CHOWDER'
(Other definitions for chowder that I've seen before include "Rich soup with fish, clams etc." , "dish in America" , "Clam stew, soup" , "possible first course?" , "Thick seafood soup" .)