Communist and American leadership in world conflict (4,3)
I believe the answer is:
cold war
'conflict' is the definition.
(cold war is a kind of conflict)
I don't understand the rest of the clue.
Can you help me to learn more?
(Other definitions for cold war that I've seen before include "Hostile period after 1945" , "Low card (anag.)" , "(Freezing?) state of hostility between nations" , "major stand-off" , "Conflict without engagement" .)