Greeting composer and setter with a barbecue (7)
I believe the answer is:
hibachi
'a barbecue' is the definition.
(Japanese cooking device)
'greeting composer and setter' is the wordplay.
'greeting' becomes 'hi' (hi is a kind of greeting).
'composer' becomes 'Bach' (Johann Sebastian Bach).
'and' says to put letters next to each other.
'setter' becomes 'I' (the person that set the crossword).
'hi'+'bach'+'i'='HIBACHI'
'with' is the link.
(Other definitions for hibachi that I've seen before include "Purpose" , "Japanese brazier used for outdoor cooking" , "Japanese portable barbecue" , "Japanese-style portable grill" .)