The President can not appoint a new judge unless a vacancy occurs or Congress creates a new position on the court. The Supreme Court is not involved in either case.
Supreme Court justices are appointed for life, but sometimes they choose to retire while they are still alive. They are not obligated to die in office.
In the Supreme Court of the United States, they're referred to as justices. The US Supreme Court has one Chief Justice, who is addressed by his full title (e.g., Chief Justice Roberts) and eight...