Hanging Dr Parrot (5)
I believe the answer is:
drape
'hanging' is the definition.
(thesaurus)
'dr parrot' is the wordplay.
'parrot' becomes 'ape' (I've seen this before).
'dr'+'ape'='DRAPE'
(Other definitions for drape that I've seen before include "Wrap loosely (with cloth)" , "Hang - curtain" , "Screen" , "Hang (cloth) in folds (on something)" , "Cover with a loose cloth" .)