Eat up, Miss Blyton (4)
I believe the answer is:
enid
'miss blyton' is the definition.
(I've seen this before)
'eat up' is the wordplay.
'eat' becomes 'dine' (to dine is to eat a meal).
'up' shows that the letters should be reversed in order (in down clue: letters go upwards).
'dine' reversed gives 'ENID'.
(Other definitions for enid that I've seen before include "- Blyton, children's writer" , "& 18 Down Children's author" , "W - - Blyton" , "Writer of children's books, d. 1968" , "Dine with this girl" .)