Fine food shop has pretty item sent to a customer (8)
I believe the answer is:
'item sent to a customer' is the definition.
(something delivered to someone)
'fine food shop has pretty' is the wordplay.
'fine food shop' becomes 'deli' (short for delicatessen).
'has' says to put letters next to each other.
'pretty' becomes 'very' (pretty can mean very or considerably).
(Other definitions for delivery that I've seen before include "Handing over - manner of speaking" , "Carriage and supply" , "that might take 3-5 days" , "Shipment" , "Address" .)