A proxy war is "a war instigated by a major power which does not itself become involved." -Oxford Dictionary
While the Cold War was so named for being a war of tension and competition, "there were real wars, sometimes called 'proxy wars' because they were fought by Soviet allies rather than the USSR itself—along with competition for influence in the Third World, and a major superpower arms race." -Library of Congress
The two most well-known proxy wars were the Vietnam and Korean Wars.