Former vice presidents can run for the president's office in future as long as they are constitutionally eligible.
It has also been a common trend for former vice-presidents to run for the president's office in the United States. According to the United States Senate official website, fourteen of the former vice presidents became president of the United States—more than half of them after a president had died.
A report published by Vox in Oct 2015 on the history of vice-presidents trying to be presidents stated that there have been 17 bids for the presidency launched after a vice presidents' term. Five vice presidents tried and failed to get their party's endorsement. An additional seven did get the endorsement but went on to lose the general election.
Only five vice presidents claimed the White House through an election: John Adams, Thomas Jefferson, and, 144 years later, George H.W. Bush. One other vice president, Richard Nixon, was eventually elected eight years after he left office.
According to Article II of the U.S. Constitution, the president must be a natural-born citizen of the United States, be at least 35 years old, and have been a resident of the United States for 14 years. In the future, as long as vice president-elect Kamala Harris fulfills the constitutional eligibility criteria to be the president, she can run for the president's office but there is no way to ascertain whether Harris has any intention to run for the president's office in the future.