Independent politician, his undoing is being full of mischief (6)
I believe the answer is:
impish
'being full of mischief' is the definition.
(thesaurus)
'independent politician his undoing' is the wordplay.
'independent' becomes 'i'.
'politician' becomes 'mp'.
'undoing' indicates an anagram.
'his' is an anagram of 'ish'.
'i'+'mp'+'ish'='IMPISH'
'is' acts as a link.
(Other definitions for impish that I've seen before include "Mischievous like small devil" , "Playful" , "Naughty" , "Teasingly mischievous" , "troublesome" .)