Bird's constant noise (4)
I believe the answer is:
crow
'bird's' is the definition.
(crow is a kind of bird)
'constant noise' is the wordplay.
'constant' becomes 'c' (mathematical abbreviation).
'noise' becomes 'row'.
'c'+'row'='CROW'
(Other definitions for crow that I've seen before include "Brag; carrion bird" , "Bird - birdcall" , "Express gleeful triumph" , "Boast, swagger, triumph" , "one often getting stoned!" .)