Offensive rumour about retired doctor (7)
I believe the answer is:
noisome
'offensive' is the definition.
('noisome' can be similar in meaning to 'offensive')
'rumour about retired doctor' is the wordplay.
'rumour' becomes 'noise' (I've seen this before).
'about' is an insertion indicator.
'retired doctor' becomes 'om' (I can't justify this - if you can you should give a lot more credence to this answer).
'noise' going around 'om' is 'NOISOME'.
Can you help me to learn more?
(Other definitions for noisome that I've seen before include "Humming" , "Offensively smelly" , "Disgusting to sight or smell" , "Obnoxious" , "Foul-smelling, noxious" .)