Cool-headed old Waugh calls for unarmed conflict (4,3)
I believe the answer is:
cold war
'unarmed conflict' is the definition.
'cold war' can be an answer for 'conflict' (cold war is a kind of conflict). I'm not sure about the 'unarmed' bit.
'cool-headed old waugh calls for' is the wordplay.
'cool-headed old' becomes 'cold' (synonyms. I am not sure about the 'cool-headed' bit.).
'calls for' shows a homophone (sound like) (I've seen 'called for' mean this).
'waugh' is a homophone of 'war'.
'cold'+'war'='COLD WAR'
Can you help me to learn more?
(Other definitions for cold war that I've seen before include "East West tension" , "(Freezing?) state of hostility between nations" , "Chilly hostility between nations without actual fighting" , "Hostile period after 1945" , "Conflict without engagement" .)