Broadcast freed by a student of government (7)
I believe the answer is:
federal
'government' is the definition.
(federal government is a kind of government)
'broadcast freed by a student' is the wordplay.
'broadcast' indicates anagramming the letters.
'by' means one lot of letters go next to another.
'student' becomes 'l' (as in L-plates for learner drivers).
'freed' anagrammed gives 'feder'.
'feder'+'a'+'l'='FEDERAL'
'of' acts as a link.
(Other definitions for federal that I've seen before include "in league" , "National, in the US" , "Relating to a treaty" , "like the USA" , "(Of a union or government) involving states voluntarily joined together for common purposes" .)