Dramatic incident following live programme that's indecent (7)
I believe the answer is:
obscene
'indecent' is the definition.
(similar in meaning)
'dramatic incident following live programme' is the wordplay.
I cannot quite see how this works, but
'incident' could be 'scene' (scene is a kind of incident) and 'scene' is present in the answer.
The remaining letters 'ob' is a valid word which might be clued in a way I don't understand.
This may be the basis of the clue (or it may be nonsense).
'that's' acts as a link.
Can you help me to learn more?
(Other definitions for obscene that I've seen before include "Prurient" , "off colour?" , "Sexually offensive" , "Rude" , "Abhorrent or lewd" .)