Singer? Just beat it! (5)
I believe the answer is:
pipit
'singer?' is the definition.
(pipit is a kind of birdanimal)
'beat it' is the wordplay.
'beat' becomes 'pip' (pipping is a kind of beating).
'pip'+'it'='PIPIT'
'just' acts as a link.
(Other definitions for pipit that I've seen before include "Bird of meadow, tree, or rock" , "Lark-like bird" , "Titlark" , "Small bird of rock or meadow" , "Songbird of open country" .)