On air, broadcast covering Democrat's decree (6)
I believe the answer is:
ordain
'decree' is the definition.
(ordaining is a kind of decreeing)
'on air broadcast covering democrat's' is the wordplay.
'broadcast' is an anagram indicator.
'covering' means one lot of letters goes inside another.
'democrat' becomes 'd'.
'on'+'air'='onair'
'onair' with letters rearranged gives 'orain'.
'orain' enclosing 'd' is 'ORDAIN'.
(Other definitions for ordain that I've seen before include "Either prescribe" , "Confer holy orders upon" , "frock" , "Invest with priestly authority" , "Invest with ministerial authority" .)