Monster put on wrapping paper (6)
I believe the answer is:
dragon
'monster' is the definition.
(dragon is a kind of monster)
'put on wrapping paper' is the wordplay.
'put on' becomes 'don' (synonyms).
'wrapping' indicates putting letters inside.
'paper' becomes 'rag' (rag paper is a kind of paper).
'don' going around 'rag' is 'DRAGON'.
(Other definitions for dragon that I've seen before include "Formidable woman" , "St George slew one" , "Fiery monster" , "Fire-breathing beast" , "Mythical reptile" .)