One politician on right is about to shut up? (8)
I believe the answer is:
imprison
'shut up?' is the definition.
(thesaurus)
'one politician on right is about' is the wordplay.
'one politician' becomes 'imp' (I've seen this in other clues**).
'right' becomes 'r' (common abbreviation).
'about' is an anagram indicator.
'on'+'r'+'is'='onris'
'onris' anagrammed gives 'rison'.
'imp'+'rison'='IMPRISON'
'to' is the link.
(Other definitions for imprison that I've seen before include "Detain" , "Incarcerate" , "Bang up" , "Put away" , "shut up" .)