Offensive racket outside room periodically (7)
I believe the answer is:
noisome
'offensive' is the definition.
(similar in meaning)
'racket outside room periodically' is the wordplay.
'racket' becomes 'noise' (racket can mean a loud noise).
'outside' indicates putting letters inside (some letters go outside others).
'periodically' indicates alternate letters (letters must be selected 'every so often').
The alternate letters of 'room' are 'om'.
'noise' placed around 'om' is 'NOISOME'.
(Other definitions for noisome that I've seen before include "Odorous" , "Nauseating" , "Foul; putrid" , "Foul-smelling - semi-Ono (anag)" , "Repugnant" .)