Broadcast screen went off once (4)
I believe the answer is:
hied
'went off once' is the definition.
('hie' could historically mean to go quickly)
'broadcast screen' is the wordplay.
'broadcast' indicates a 'sounds like' (homophone) clue (how the word might sound on the radio or TV).
'screen' becomes 'hide' (hide can mean to screen or cover up).
'hide' sounds like 'HIED'.
(Other definitions for hied that I've seen before include "Went quickly (archaic)" , "Hurried" , "Rushed" , "Hastened" , "Ran" .)