I clam up in broadcast relating to local government (9)
I believe the answer is:
municipal
'relating to local government' is the definition.
(I've seen this before)
'i clam up in broadcast' is the wordplay.
'broadcast' indicates an anagram.
'i'+'clam'+'up'+'in'='iclamupin'
'iclamupin' anagrammed gives 'MUNICIPAL'.
(Other definitions for municipal that I've seen before include "Run by the council" , "Of local council" , "Borough" , "Relating to a town or district" , "of one's town" .)