Deny outrage followed a denial was inoffensive (7)
I believe the answer is:
anodyne
'inoffensive' is the definition.
(I've seen this in another clue)
'deny outrage followed a denial' is the wordplay.
'deny outrage' becomes 'dyne' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'followed' means one lot of letters go next to another (some letters go after others).
'denial' becomes 'no' (no is a kind of denial).
'a'+'no'='ano'
'dyne' after 'ano' is 'ANODYNE'.
'was' acts as a link.
Can you help me to learn more?
(Other definitions for anodyne that I've seen before include "painkiller" , "Avoiding controversy - done any (anag)" , "Pain relieving" , "Palliative (agent)" , "Annoyed, being pain reliever" .)