Most U.S. Presidents have been fairly elderly by the time they completed their term and have gone into a less demanding line of work (either lecturing or serving on corporate boards of directors.)
There is no law forbidding a former President from running for office, unless the President was impeached and convicted (which has never happened), and excepting the constitutional provision that after serving two terms, a person is ineligible to be President again.
In the 19th Century, I believe John Quincy Adams was elected to the House of Representatives after his term expired. In the 20th Century, William Howard Taft was appointed Chief Justice after he left the White House.
Here’s the rundown of 20th Century Presdients after leaving office, as best as I can recall.
T. Roosevelt – ran for President again on a 3rd party ticket, was wounded in an assasination attempt.
Taft – was appointed Chief Justice
Wilson – was in poor health when he left office
Harding – died in office
Coolidge – was 56 when he left office. Retired from public life and died 4 years later.
Hoover – served on commissions for Truman and Eisenhower
F. D.Roosevelt – died in office
Truman – was nearly 70 when he left office, retired from public life
Eisenhower – was 70 when he left office and had health problems
Kennedy – died in office
Johnson – was 61 when he left office, but had a history of heart problems. He retired and died within 5 years.
Nixon – resigned office and mostly retired from public life, except for speaking engagements.
Ford – was 63 when he was defeated for re-election. There was some talk about him running for Vice-President with Ronald Reagan, but that didn’t materialize. He then mostly retired from public life.
Carter – was 56 when he left office. Has served as a U.S. envoy several times, but mainly devotes his time to Habitat for Humanity and other charitable organizations.
Reagan – was 77 when he left office, had survived an assasination attempt and surgery
George H. W. Bush – was 58 when he left office. He said repeatedly during Clinton’s term that a former President should not speak out publicly and risk undermining the authority of a sitting President.
Clinton – was 52 when he left office and now is mostly known for public speaking.
So there were only a few Presidents who were young and healthy enough to remain in public life. I suspect many, like George H.W. Bush felt constrained from being in a public position where they would be expected to comment on their successors.