Cheese could make female fed up (4)
I believe the answer is:
feta
'cheese' is the definition.
(type of cheese)
'female fed up' is the wordplay.
'female' becomes 'f' (common abbreviation).
'fed' becomes 'ate' ('eat' can be a synonym of 'feed').
'up' says the letters should be written in reverse (in down clue: letters go upwards).
'ate' backwards is 'eta'.
'f'+'eta'='FETA'
'could make' acts as a link.
(Other definitions for feta that I've seen before include "Greek cheese from goat or sheep milk" , "food there" , "Type of cheese" , "Greek 8 across" , "Salty Greek cheese" .)