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' is an insertion indicator.
'a politician' becomes 'MP' (Member of Parliament).
'jude' with letters rearranged gives 'jued'.
'jued' placed around 'mp' is 'JUMPED'.
'to get' acts as a link.
(Other definitions for jumped that I've seen before include "Made a leap" , "Leapt" .)