Terrible-sounding US politician’s jewelled headband (6)
I believe the answer is:
diadem
'jewelled headband' is the definition.
(I've seen this before)
'terrible-sounding us politician's' is the wordplay.
'terrible' becomes 'dire' (synonyms).
'sounding' shows a homophone (sound like).
'us politician' becomes 'dem' (short for Democrat).
'dire' is a homophone of 'dia'.
'dia'+'dem'='DIADEM'
(Other definitions for diadem that I've seen before include "Jewelled headband" , "Crown or headband worn as symbol of sovereignty" , "Ornamental jewelled headdress" , "Royal power" , "Crown or headband for sovereign" .)