Greek character flies over horse (7)
I believe the answer is:
mustang
'horse' is the definition.
(I know that mustang is a type of pony)
'greek character flies over' is the wordplay.
'greek character' becomes 'mu' (letter from the Greek alphabet).
'flies' becomes 'gnats'.
'over' shows that the letters should be reversed in order.
'gnats' backwards is 'stang'.
'mu'+'stang'='MUSTANG'
(Other definitions for mustang that I've seen before include "creature" , "Ford car, first produced in 1964" , "Hardy wild horse of the American western plains" , "Wild or half-wild horse" , "Trotter" .)