Brown’s undertaking involving king’s broadcast (12)
I believe the answer is:
transmission
'broadcast' is the definition.
(I've seen this before)
'brown's undertaking involving king's' is the wordplay.
'brown's' becomes 'tans' (tan is a kind of brown).
'undertaking' becomes 'mission' (I've seen this in other clues).
'involving' indicates putting letters inside.
'king' becomes 'r' (r is abbreviation for rex).
'tans'+'mission'='tansmission'
'tansmission' placed around 'r' is 'TRANSMISSION'.
(Other definitions for transmission that I've seen before include "The sending of a radio signal" , "A broadcast programme" .)