American tucked into his exotic dish (5)
I believe the answer is:
sushi
'dish' is the definition.
(sushi is a kind of dish)
'american tucked into his exotic' is the wordplay.
'american' becomes 'us' (abbreviation for United States).
'tucked into' indicates putting letters inside.
'exotic' indicates an anagram.
'his' is an anagram of 'shi'.
'us' put inside 'shi' is 'SUSHI'.
(Other definitions for sushi that I've seen before include "Rice, seafood cuisine" , "Oriental food" , "Japanese cuisine" , "rice dishes" , "Food from Japan" .)