Cafe taken with dairy product (4)
I believe the answer is:
feta
'dairy product' is the definition.
(type of cheese)
'cafe taken with' is the wordplay.
'with' indicates a hidden word.
'FETA' is hidden within 'cafe taken'.
(Other definitions for feta that I've seen before include "Eastern Mediterranean cheese" , "Goat's or sheep's milk cheese" , "Salty Greek cheese" , "Type of cheese" , "Low-fat cheese" .)