Finally safe from you, Big Bird! (3)
I believe the answer is:
emu
'big bird' is the definition.
(type of large bird)
'finally safe from you' is the wordplay.
'finally' suggests the final letters.
The final letters of 'safe from you' are 'EMU'.
(Other definitions for emu that I've seen before include "Aussie runner" , "Flightless Aus. bird" , "Flightless bird of Australia, like ostrich" , "Parky's nemesis" , "Ratite" .)