Greek character fed up (3)
I believe the answer is:
eta
'greek character' is the definition.
(letter from the Greek alphabet)
'fed up' is the wordplay.
'fed' becomes 'ate' ('eat' can be a synonym of 'feed').
'up' is a reversal indicator (in down clue: letters go upwards).
'ate' written backwards gives 'ETA'.
(Other definitions for eta that I've seen before include "Letter from abroad" , "when you can hope to receive it" , "when it might reach us?" , "Something like 10 [RHO]" , "Greek letter - time due (abbr)" .)