Dick Grayson wound up being this to Jean Paul-Valley. In "Prodigal", the direct followup to the "Knightfall" saga, Bruce takes a sabbatical not long after reclaiming the mantle of the Bat from Valley in order to avoid burning himself out again. Dick takes over during in his absence and explicitly makes sure to remind everyone that there's still a Batman who can show compassion and has rules when it comes to the law.
The Flash: Owen Mercer, the son of the first Captain Boomerang, tried to be one of these.
Injustice 2: You wouldn't think Superman would need one of these, but, Superboy Conner Kent ends up donning the classic suit (red trunks and all) years after the original went Knight Templar. Similarly, seeing how far Superman has fallen, Supergirl ultimately decides to bring honor back to the House of El.
Justice League of America: The female Dr. Light, who (like the Toyman example above) is a Japanese genius. She's also a scientist and Mama Bear - as opposed to the first Dr. Light, who was a man, a villain, and a rapist (by retcon).
Justice Society of America: The Golden Age villain Brain Wave had a son that called himself Brain Wave Jr. and became a member of Infinity, Inc.. Of course, he's now gone a long way from being the hero that he was.
Kingdom Come: One story had Iris "Kid Flash" West encounter the Fiddler's great-grandson, Iowa Bowin, who believed his ancestor had "a headful of bad wiring", and wants to use his guitar version of Isaac's weaponized violin to be a hero.
This is the basic idea behind Brainiac 5, descendant of Superman's villain Brainiac. (There are intervening Brainiacs of varied morality, but they weren't really focused on until well after B5 had been introduced.)
Also from the Legion, Danielle Foccart assumed the codename "Computo" in the V4 era when she gained Technopathic powers — after the villainous AI that possessed her in her first appearance (her brother Jacques' origin as the second Invisible Kid).
Superman: One version of Toyman is a young Japanese genius, while the other versions of the character are all villains. Unfortunately he, like all other versions, turned out to be a super-advanced android, created by the one and only original Toyman. However, the New 52Cosmic Retcon saw him back as a human and as a heroic Toyman.
Teen Titans: The original Terra turned out to be The Mole for the team and an unrepentant villain. Her first successor was a deliberate attempt to show a heroic version of Terra, to the point where some DC editors and writers even wanted her to be the original resurrected (this wound up averted in the end). The third Terra (who was originally planned to be an unrelated character) was even more of an example, as she lacked the second Terra's identity crisis issues and the original's sociopathy, and was a much more idealistic hero without much angst at all.
