He bills me incorrectly to decorate (9)
I believe the answer is:
embellish
'decorate' is the definition.
(I know that decorate can be written as embellish)
'he bills me incorrectly' is the wordplay.
'incorrectly' indicates anagramming the letters (I've seen this in other clues).
'he'+'bills'+'me'='hebillsme'
'hebillsme' anagrammed gives 'EMBELLISH'.
'to' is the link.
(Other definitions for embellish that I've seen before include "Make more interesting by adding details that may be untrue" , "Add false details" , "Improve story by adding invented details" , "Adorn" , "deck?" .)