Female gobbled up cheese (4)
I believe the answer is:
feta
'cheese' is the definition.
(I've seen this before)
'female gobbled up' is the wordplay.
'female' becomes 'f' (abbreviation).
'gobbled up' becomes 'eta' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'f'+'eta'='FETA'
Can you help me to learn more?
(Other definitions for feta that I've seen before include "White and salty goat or sheep cheese" , "Low-fat cheese" , "food there" , "Type of cheese" , "Greek salad cheese" .)