The setter tucked into pieces on dog's dish (4,4)
I believe the answer is:
chow mein
'dish' is the definition.
(chow mein is a kind of dish)
'the setter tucked into pieces on dog's' is the wordplay.
'the setter' becomes 'I' (the person that set the crossword).
'tucked into' means one lot of letters goes inside another.
'pieces' becomes 'men' (man can mean a chess piece).
'on' says to put letters next to each other.
'dog' becomes 'chow' (short for chow chow).
'i' placed within 'men' is 'mein'.
'mein' after 'chow' is 'CHOW-MEIN'.
(Other definitions for chow mein that I've seen before include "Chinese dish of noodles, meat and veg" , "Chinese/US noodle dish" , "Hi cowmen, fancy a Chinese dish?" , "Chinese-style noodle dish" , "Chinese-American dish" .)