Partially consumed a mild cheese (4)
I believe the answer is:
edam
'cheese' is the definition.
(I've seen this before)
'partially consumed a mild' is the wordplay.
'partially' says the answer is hidden in the clue.
'EDAM' is hidden within 'consumed a mild'.
(Other definitions for edam that I've seen before include "Type of cheese" , "Madeinto popular cheese" , "Netherlands cheese" , "Mild yellow Dutch cheese" , "Dairy product" .)