If the Vice President resigns, the President will remain in office and the Vice Presidency will become vacant. The Constitution provides that the Vice President succeeds the President in cases of removal, death, resignation, or disability, but it makes no provision for filling vacancies in the vice presidency. However, the Twenty-Fifth Amendment to the United States Constitution clarifies that in case of the removal of the President from office or of his death or resignation, the Vice President shall become President.
If the Vice President resigns, the President will remain in office, and the Vice Presidency will become vacant. The Presidential Succession Act of 1947 places the Speaker of the House and President Pro Tempore of the Senate in first and second place, followed by the Cabinet, as before.
If the Vice President resigns, the President can nominate a Vice President who shall take office upon confirmation by a majority vote of both Houses of Congress.