What role is exemplified by the President greeting the Prime Minister of Great Britain?

Chief Diplomat (Thought not used, this is something like a Presidential Ambassador). The role of the U. S. President as the head of the executive office of the United States and top leader of the country serves as the role of the Chief Diplomat in greeting and meeting with the heads of states of other countries. He is the top representative of the American people to other nations in this role and the various others attributed to the position of the U. S. President.