A small bird, an old giant (5)
I believe the answer is:
titan
'old giant' is the definition.
(I've seen this before)
'a small bird an' is the wordplay.
'a small bird' becomes 'tit' (I've seen this in another clue).
'tit'+'an'='TITAN'
(Other definitions for titan that I've seen before include "Goddess" , "One of the first pantheon of Greek deities" , "Mythological giant" , "Atlas, possibly" , "bigwig" .)