Swamp creature caught by enormous bird (4)
I believe the answer is:
croc
'swamp creature' is the definition.
(short for crocodile)
'caught by enormous bird' is the wordplay.
'caught' becomes 'c' (cricket abbreviation).
'by' says to put letters next to each other.
'enormous bird' becomes 'roc' (I've seen this before).
'c'+'roc'='CROC'
(Other definitions for croc that I've seen before include "creature heard to be a vicious one" , "Snapper" , "Predatory reptile (informal)" , "Fierce reptile" , "Wild animal" .)