Eat up girl! (4)
I believe the answer is:
enid
'girl' is the definition.
(girl's name)
'eat up' is the wordplay.
'eat' becomes 'dine' (to dine is to eat a meal).
'up' says the letters should be written in reverse (in down clue: letters go upwards).
'dine' reversed gives 'ENID'.
(Other definitions for enid that I've seen before include "Lady" , "Writer of children's books, d. 1968" , "Dine with Ms blyton, writer" , "Dine with this girl" , "Arthurian wife" .)