Started to get Jude agitated about a politician (6)
I believe the answer is:
jumped
'started' is the definition.
(jumping is a kind of starting)
'jude agitated about a politician' is the wordplay.
'agitated' is an anagram indicator.
'about' indicates putting letters inside.
'a politician' becomes 'mp'.
'jude' anagrammed gives 'jued'.
'jued' going around 'mp' is 'JUMPED'.
'to get' is the link.
(Other definitions for jumped that I've seen before include "Made a leap" , "Leapt" .)