Broadcast rude tape about king's shift (9)
I believe the answer is:
departure
'shift' is the definition.
(I've seen this before)
'broadcast rude tape about king's' is the wordplay.
'broadcast' indicates anagramming the letters.
'about' is an insertion indicator.
'king' becomes 'r' (r is abbreviation for rex).
'rude'+'tape'='rudetape'
'rudetape' with letters rearranged gives 'departue'.
'departue' placed around 'r' is 'DEPARTURE'.
(Other definitions for departure that I've seen before include "Exodus" , "shift" , "Lucky" , "Not the usual" , "new approach" .)