Disparage one fireplace behind study (9)
I believe the answer is:
denigrate
'disparage' is the definition.
(I know that denigrate is a more specific form of disparage)
'one fireplace behind study' is the wordplay.
'one' becomes 'i' (Roman numeral).
'fireplace' becomes 'grate' (grate can mean a fireplace).
'behind' means one lot of letters go next to another.
'study' becomes 'den' (term for a study or office).
'i'+'grate'='igrate'
'igrate' put after 'den' is 'DENIGRATE'.
(Other definitions for denigrate that I've seen before include "Slight" , "Defame" , "Criticise, belittle" , "put down" , "Unfairly criticise" .)