Get ready for Hillary Clinton 4.0. More than 30 years in the making, this new version of Mrs. Clinton, when she runs for president in 2020, will come full circle—back to the universal-health-care-promoting progressive firebrand of 1994. True to her name, Mrs. Clinton will fight this out until the last dog dies. She won’t let a little thing like two stunning defeats stand in the way of her claim to the White House.

It’s been quite a journey. In July 1999, Mrs. Clinton began her independent political career on retiring Sen....