Tailless bird caught reptile (4)
I believe the answer is:
croc
'reptile' is the definition.
(short for crocodile)
'tailless bird caught' is the wordplay.
'tailless' means to remove the last letter (the tail of the word is removed).
'bird' becomes 'crow' (crow is a kind of bird).
'caught' becomes 'c' (cricket abbreviation).
'crow' with its final letter removed is 'cro'.
'cro'+'c'='CROC'
(Other definitions for croc that I've seen before include "Snapper" , "African beast; sounds like piece of pot" , "Small animal" , "Short reptile" , "Dangerous reptile" .)