Reptile beginning to chase enormous bird (4)
I believe the answer is:
croc
'reptile' is the definition.
(short for crocodile)
'beginning to chase enormous bird' is the wordplay.
'beginning to' says to take the initial letters.
'enormous bird' becomes 'roc' (mythical giant bird).
The initial letter of 'chase' is 'c'.
'c'+'roc'='CROC'
(Other definitions for croc that I've seen before include "Dangerous reptile" , "Fierce reptile" , "that might be sitting on your foot" , "Small animal" , "Short reptile" .)