No former Presidential nominee has later been nominated for Vice President, but Ronald Reagan and Gerald Ford briefly discussed the possibility of former President Ford running as Reagan’s Vice President in 1980. Although it didn’t happen and it was only briefly considered, Reagan was serious enough about it that he and Ford had preliminary discussions about how big Ford’s role would have been if it had happened.
I’m not sure if this goes along with what you’re asking, but there are two Vice Presidents who served as VP under more than one President. George Clinton was President Jefferson’s second term VP (1805-1809) and became James Madison’s running mate in 1808. John C. Calhoun was John Quincy Adams’s VP (1825-1829) and was elected VP again in 1828 alongside Andrew Jackson.
Again, I’m not sure if this fits your question either, but Thomas A. Hendricks was an unsuccessful candidate for Vice President in 1876 (alongside Samuel J. Tilden in that disputed election), but eight years later he won the Vice Presidency after all as Grover Cleveland’s first term running mate.