After serving it up, consumed fine Greek speciality (4)
I believe the answer is:
feta
'greek speciality' is the definition.
'after serving it up consumed fine' is the wordplay.
'after serving it up' shows that the letters should be reversed in order.
'consumed' becomes 'ate' (eating is a kind of consuming).
'fine' becomes 'f' (abbreviation).
'ate'+'f'='atef'
'atef' backwards is 'FETA'.
(Other definitions for feta that I've seen before include "Soft Greek cheese" , "White Greek cheese" , "Crumbly Greek cheese" , "Greek 8 across" , "10 down cheese" .)