Offensive din carries over miles (7)
I believe the answer is:
noisome
'offensive' is the definition.
(I know that offensive can be written as noisome)
'din carries over miles' is the wordplay.
'din' becomes 'noise' (a din is a noisy disturbance).
'carries' means one lot of letters goes inside another (inserted letters carried inside).
'over' becomes 'o' (cricket abbreviation).
'miles' becomes 'm' (common abbreviation).
'o'+'m'='om'
'noise' placed around 'om' is 'NOISOME'.
(Other definitions for noisome that I've seen before include "Harmful - offensive" , "Harmful - noxious" , "Unpleasantly smelling" , "Moonies (anag.)" , "noxious smells" .)