Yes, unlike the presidency, if the Vice President leaves office (dies, or like Agnew, reigns), nobody immediately moves up to fill the position. A new Vice President has to be nominated and confirmed by the senate. That is what was happening in the gap between Agnew and Ford.

Interestingly, there have been much longer times without a Vice President, (generally occurring after the death of a president). Harry Truman, for example served without a VP after succeeding FDR. He would not have one until the next election nearly three years after taking the office.

If there is no Vice President and the current president leaves office, it passes to the next in line, the speaker of the house.