Broadcast shows monarch's head in carriage (8)
I believe the answer is:
transmit
'broadcast' is the definition.
('transmit' can be a synonym of 'broadcast')
'monarch's head in carriage' is the wordplay.
'head' says to take the initial letters.
'in' indicates putting letters inside.
'carriage' becomes 'transit' (I've seen this before).
The initial letter of 'monarchs' is 'm'.
'm' going inside 'transit' is 'TRANSMIT'.
'shows' is the link.
(Other definitions for transmit that I've seen before include "Communicate (an idea)" , "Pass or hand on" , "Send from one to another, electronically say" , "Pass on (message)" , "F. name; Hamlet (anag.)" .)