Fancy pigeon Greek character needed on top (3)
I believe the answer is:
nun
'fancy pigeon' is the definition.
(nun is a breed of fancy pigeon)
'greek character needed on top' is the wordplay.
'greek character' becomes 'nu' (letter from the Greek alphabet).
'on top' suggests taking the first letters.
The initial letter of 'needed' is 'n'.
'nu'+'n'='NUN'
(Other definitions for nun that I've seen before include "Carmelite, for example" , "One who's taken vows" , "Religious sister" , "Woman with a habit" , "One in holy order" .)