Caught parrot in cloak (4)
I believe the answer is:
cape
'cloak' is the definition.
(I know that cape is a type of cloak)
'caught parrot' is the wordplay.
'caught' becomes 'c' (cricket abbreviation).
'parrot' becomes 'ape' (both can mean to imitate).
'c'+'ape'='CAPE'
'in' acts as a link.
(Other definitions for cape that I've seen before include "Short cloak" , "Loose cloak or promontory" , "Batman has one" , "Shoulders? They're covered in it" , "Outer garment" .)