Briefly agitate cool war leader (9)
I believe the answer is:
churchill
'war leader' is the definition.
(Winston Churchill)
'briefly agitate cool' is the wordplay.
I cannot quite see how this works, but
'cool' could be 'chill' (synonyms) and 'chill' is found within the answer.
This may be the basis of the clue (or it may be nonsense).
Can you help me to learn more?
(Other definitions for churchill that I've seen before include "Wartime PM" , "Old leader" , "13 [THIRD REICH] 's nemesis" , "Winston . . . . . . . . ., English PM war leader" , "He offered the British people "nothing but blood, toil, tears and sweat"" .)