Giant bird primarily attacking nestlings (5)
I believe the answer is:
titan
'giant' is the definition.
(titans are giant mythological creatures)
'bird primarily attacking nestlings' is the wordplay.
'bird' becomes 'tit' (tit is a kind of bird).
'primarily' indicates taking the first letters.
The first letters of 'attacking nestlings' is 'an'.
'tit'+'an'='TITAN'
(Other definitions for titan that I've seen before include "One of the first pantheon of Greek deities" , "Huge(ly important) type" , "one of great importance" , "Very strong or important person" , "Goddess" .)