Second channel covering Duke's outrage (7)
I believe the answer is:
scandal
'outrage' is the definition.
(I know that outrage can be written as scandal)
'second channel covering duke's' is the wordplay.
'second' becomes 's' (common abbreviation).
'channel' becomes 'canal' (synonyms).
'covering' means one lot of letters goes inside another.
'duke' becomes 'd' (abbreviation).
'canal' enclosing 'd' is 'candal'.
's'+'candal'='SCANDAL'
(Other definitions for scandal that I've seen before include "Event causing public outrage" , "Public outrage; gossip" , "Public disgrace" , "Shocking thing" , "content of 3 [RED TOPS]?" .)