Greek character flies over for horse (7)
I believe the answer is:
mustang
'for horse' is the definition.
(mustang is a kind of horse)
'greek character flies over' is the wordplay.
'greek character' becomes 'mu' (letter from the Greek alphabet).
'flies' becomes 'gnats'.
'over' is a reversal indicator.
'gnats' written backwards gives 'stang'.
'mu'+'stang'='MUSTANG'
(Other definitions for mustang that I've seen before include "Ford car, first produced in 1964" , "one running wild" , "Small, wild US horse" , "Small feral horse of the US" , "SW US wild horse" .)