According to the 25th Amendment to the Constitution (1967), If a vice president resigns or he cannot continue in charge, the then President has to select a new candidate to cover the vacancy. The nominee must be approved by the House of Representatives and the Senate by majority.
The correct answer to this open question is the following.
In the case of a resignation of the Vicepresident of the United States, the 25th Amendment to the United States Constitution has the answer in section 2. It says that the President of the US has to nominate a new Vicepresident for the remaining time of the presidency term. His candidate must be approved by a majority vote in Congress.
