Head of state on the radio (4)
I believe the answer is:
main
'head' is the definition.
(thesaurus)
'state on the radio' is the wordplay.
'state' becomes 'maine' (US state).
'on the radio' shows a homophone (sound like).
'maine' is a homophone of 'MAIN'.
'of' acts as a link.
(Other definitions for main that I've seen before include "(The mighty) sea" , "river in Germany" , "location for 9 [ARMADA]" , "source of gas" , "Chief in importance" .)