Emulate a bird: leave in haste (4,2)
I believe the answer is:
beat it
'leave in haste' is the definition.
'beat it' can be an answer for 'leave' (I've seen this before). I am unsure of the 'in haste' bit.
'emulate a bird' is the wordplay.
'emulate' becomes 'bea' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'a bird' becomes 'tit' (tit is a kind of bird).
'bea'+'tit'='BEAT IT'
Can you help me to learn more?
(Other definitions for beat it that I've seen before include "Scarper" , "try out drum kit?" , "Get going" , "Make off hastily" , "Slang order to go away, get lost" .)