Doctor with parrot in shroud (5)
I believe the answer is:
drape
'shroud' is the definition.
(thesaurus)
'doctor with parrot' is the wordplay.
'doctor' becomes 'Dr' (abbreviation).
'with' says to put letters next to each other.
'parrot' becomes 'ape' (both can mean to imitate).
'dr'+'ape'='DRAPE'
'in' is the link.
(Other definitions for drape that I've seen before include "Loose fabric cover" , "Cover with a loose cloth" , "Cover loosely with cloth" , "Hang (cloth) in folds (on something)" , "Hang - curtain" .)