Incite riot ultimately -- hype old politician first (6)
I believe the answer is:
prompt
'incite' is the definition.
(I know that incite can be written as prompt)
'riot ultimately hype old politician first' is the wordplay.
'ultimately' says to take the final letters.
'hype' becomes 'PR' (abbreviation for public relations).
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'politician' becomes 'MP' (Member of Parliament).
'first' is a charade indicator (letters next to each other).
The last letter of 'riot' is 't'.
'pr'+'o'+'mp'='promp'
't' put after 'promp' is 'PROMPT'.
(Other definitions for prompt that I've seen before include "Precisely on time" , "Bang on" , "Cause; done at once" , "Remind (actor) of lines" , "keeping to the right time" .)