Mute Republican gets a scarf (7)
I believe the answer is:
muffler
'a scarf' is the definition.
(I know that muffler is a type of scarf)
'mute republican' is the wordplay.
'mute' becomes 'muffle' (synonyms).
'republican' becomes 'r' (abbreviation).
'muffle'+'r'='MUFFLER'
'gets' is the link.
(Other definitions for muffler that I've seen before include "Warming garment" , "Kind of scarf" , "Sound deadener" , "Thick scarf - silencer (US)" , "Wrap or scarf worn round the neck" .)