Sound around the centre of Rome is offensive (7)
I believe the answer is:
noisome
'offensive' is the definition.
('noisome' can be similar in meaning to 'offensive')
'sound around the centre of rome' is the wordplay.
'sound' becomes 'noise' (noising is a kind of sounding**).
'around' means one lot of letters goes inside another.
'the centre of' says to take the centre.
The central letters of 'rome' are 'om'.
'noise' enclosing 'om' is 'NOISOME'.
'is' is the link.
(Other definitions for noisome that I've seen before include "Obnoxious" , "Humming" , "Moonies (anag.)" , "Harmful to health; disgusting" , "Offensively smelly" .)