What may restock food shop excessively (8)
I believe the answer is:
Here is my best explanation:
'what may restock' is the definition.
'food shop excessively' is the wordplay.
'food shop' becomes 'deli' ('deli' can be a synonym of 'food shop').
'excessively' becomes 'very'.
(Other definitions for delivery that I've seen before include "A handing over of goods", "useful service for the housebound", "Throw of a cricket ball", "Style of speaking", "Address", "style", "Manner of making speech or bowling a ball", "Act of giving birth", "Carriage and supply" and "Chinaman, perhaps".)