Angry speech managed to stop former Conservative leader (8)
I believe the answer is:
harangue
'angry speech' is the definition.
(harangue means a long, angry speech)
'managed to stop former conservative leader' is the wordplay.
'managed' becomes 'ran' (both can mean organised or was in charge of).
'to stop' means one lot of letters goes inside another (stopping can mean blocking a gap).
'former conservative leader' becomes 'Hague' (William Hague, former Conservative Party leader).
'ran' put inside 'hague' is 'HARANGUE'.
(Other definitions for harangue that I've seen before include "'Loud, long diatribe (8)'" , "A lengthy speech or scolding" , "Loud angry speech" , "Exhortation" , "Deliver a forceful speech" .)