Mentor's New Hope

Many years ago a great teacher oversaw a promising young pupil. It went bad, probably because he turned to evil or ended up showing his true colors, maybe even becoming the Big Bad. As the Master Apprentice Chain continues there's now a young hero being trained by the elderly Mentor. The Hero might have been Desperately Looking for a Purpose In Life so he feels like he fits somewhere when he hears in back story how his overseer/teacher also trained another some years ago, but that pupil went to The Dark Side and became the antagonist of the story. Now the teacher plans to use his second chance and hopes that this chosen one, who is the current protagonist, can stay good.

This is what might come after A Pupil of Mine Until He Turned to Evil. Compare The Three Faces of Adam.

Anime

 * Fatal Fury: In the anime adaptation, Tung Fu Ru was sempai to Jeff Bogard and Geese Howard. However, Geese felt slighted when Tung chose Jeff as his successor murdered him in retaliation. Years later, Tung takes Terry Bogard as his new pupil, and trains him in order to avenge Jeff's death.
 * This is different from the games account of Jeff's murder, which has Geese kill Jeff to prevent him from entering the King of Fighters tournament and possibly uncovering his schemes. This is shown in Art of Fighting 2's "true ending", which is obtained by defeating Geese.

Comic Books

 * The old wizard Shazam gave an Egyptian Teth-Adam (Mighty Adam) the same powers he later gave Captain Marvel, but Teth-Adam had a Face Heel Turn so Shazam renamed him Black Adam and sent him 5000 light-years from Earth.

Film

 * Of Star Wars A New Hope, there's Luke being taught by Obi-Wan, who also taught Darth Vader before Vader went to the dark side.
 * In Kung Fu Panda Tai Lung is the first devoted pupil of Master Shifu before the story starts. Now he is the enemy of Po and the Furious Five.
 * Hercules is this to Phil in Hercules according to the latter, as he'd trained so many heroes before who "failed" to live up to their names.

Literature

 * In Harry Potter young Harry is wisely watched over by Dumbledore, who also kept a close watch over Tom Riddle before he became Lord Voldemort.
 * This is part of the back story of the novel The Giver: The Receiver of Knowledge who mentors Jonas is revealed.