Giant bird with a green tail (5)
I believe the answer is:
titan
'giant' is the definition.
(titans are giant mythological creatures)
'bird with a green tail' is the wordplay.
'bird' becomes 'tit' (tit is a kind of bird).
'with' is a charade indicator (letters next to each other).
'tail' indicates one should take the final letters.
The last letter of 'green' is 'n'.
'tit'+'a'+'n'='TITAN'
(Other definitions for titan that I've seen before include "Jupiter's largest satellite" , "Very strong or important person" , "Giant -- rocket" , "Taint in old Greek god" , "Saturn's largest satellite" .)