Broadcast by a leading Irish cardinal (5)
I believe the answer is:
aired
'broadcast' is the definition.
('aired' can be a synonym of 'broadcast')
'a leading irish cardinal' is the wordplay.
'leading' indicates taking the first letters.
'cardinal' becomes 'red' (I've seen this in other clues**).
The initial letter of 'irish' is 'i'.
'a'+'i'+'red'='AIRED'
'by' acts as a link.
(Other definitions for aired that I've seen before include "Ventilated, or hung out to dry" , "Put to dry; said publicly" , "Vented to or exposed to breeze" , "Expressed publicly" , "Exposed to breeze for freshening - say damp clothes" .)