Duke meets priest in food store (4)
I believe the answer is:
deli
'food store' is the definition.
(I've seen this in another clue)
'duke meets priest' is the wordplay.
'duke' becomes 'd' (abbreviation).
'meets' means one lot of letters go next to another.
'priest' becomes 'eli' (biblical figure).
'd'+'eli'='DELI'
'in' acts as a link.
(Other definitions for deli that I've seen before include "Exotic food shop" , "Specialised food shop" , "Fine foods shop" , "part of supermarket" , "Seller of unusual foods" .)