This trope is when even though the villain of a work is no longer around, the plot continues to be driven by things they did while alive. This can be done by his organization being taken over by someone else, his descendants being evil themselves, someone continues his plans without him, and so forth. If it's an ongoing series where one way or another every villain can be traced back to the first one despite his defeat, it's this trope.
This trope is not, however, when the original villain is still manipulating things behind the scenes. For a true Villainous Legacy, they must have actually been defeated and are no longer the main threat. If the villain somehow continues to directly act against the heroes in some manner, it is not this trope. This trope can still apply if the villain is still around, as long as they are no longer the primary antagonist of the current story.
Compare Hijacked by Ganon, As Long as There Is Evil,and My Death Is Just the Beginning, each of which can overlap with this trope. See also The Man Behind the Man, The Man Behind The Monsters, Someone to Remember Him By, Leaking Can of Evil, The Remnant, Avenging the Villain, which can be assorted ways this trope is invoked.
NOTE: Because this trope focuses on a villain being behind other events in a series, expect unmarked spoilers.
Anime and Manga
Jojos Bizarre Adventure has main villain Dio; even after his death, his shadow looms over the Joestar, causing them and the world much trouble. Even he, however, is a result of a much more ancient evil from mesoamerica.
Digimon Savers: Even after Kurata is defeated, his genocide of Digimon makes King Drasil believe all humans are evil, and thus he attempts to destroy the human world to protect the digimon world.
The Saw series. Jigsaw is killed in Saw 3, but the series is continued on by his apprentices and the plans he's left for them to follow.
Norman Osborn had this role for decades after he "died". He had killed Spider-Man's girlfriend and created a supervillain legacy that not only included his own son, but several goblin-based villains that plagued Spidey for years. Of course, since Death Is Cheap, Osborn is back these days.
In X-Men, after Stryfe is defeated, it turns out that he has left behind a virus that spreads through humans and kills those with the x-gene, devastating mutantkind for years. Appropriately, it is referred to as the Legacy virus.
In the long-ago Back Story of the The Sharing Knife books, the ancestors of the Lakewalkers managed to kill their villainous sorcerer-king that threatened to destroy the world. However, it split into fragments and spread over most of a continent, each piece able to grow into a malice. The Lakewalkers in the books are still clearing those out, several hundred years later.
There is an entire subgenre of Star Wars Expanded Universe books dealing with the immediate aftermath of Return of the Jedi - just because the Emperor is dead doesn't mean there's nobody who is interested in continuing the Empire.
...the lies that Melkor, the mighty and accursed, Morgoth Bauglir, the Power of Terror and of Hate, sowed in the hearts of Elves and Men are a seed that does not die and cannot be destroyed; and ever and anon it sprouts anew, and will bear dark fruit even unto the latest days.
When The Shadows left the galaxy on Babylon 5, they left behind some technology, and at least one planet-killer ship—and their old Henchmen Race race the Drakh, who searched for and obtained some of these items for use in their own designs for conquest.
Warhammer 40K, Orks have a biological version of this: their corpses release spores that eventually mature into more orks, ensuring that a planet that's been attacked once will pretty much always face them from then on.
The Legend of Zelda: Skyward Sword reveals that the machinations of Ganon are the legacy of Demise, the Demon King who cursed Link and Zelda to be plagued by an incarnation of his hatred forever, manifested in Ganondorf (and perhaps others)
Ultima. Mondain is the Big Bad of the first game. The second and third games have the villains as his lover and apprentice Minax, and their creation Exodus. The fourth game requires the player to retrieve Mondain's skull, and the fifth game has the villains as manifestations of the shards of his Artifact of Doom the player destroyed in the first game. In the sixth game, the Gargoyles summoned Mondain's spirit to embody their virtue of Control, along with Minax and Exodus. Finally, the Guardian, the villain of all subsequent games from VI, was initially planned to be revealed as the combined form of the Shadowlords after they were cast into the Void, but this was axed.
In Final Fantasy VII and its expanded universe, all major villains trace themselves back to Jenova, an Eldritch Abomination who tried to destroy the planet 2000 years ago. Jenova was found by Shinra, and the lab experiments produced by tinkering with her cells serve as the villains of the series, along with a few of the scientists who did said tinkering.
Non-character example in Fallout. The Big Bad of the first game, The Master, was using the Forced Evolutionary Virus to mutate humans. The villains of the second game excavated the ruins of his lair to retrieve the FEV for their own uses, and the villains of the third synthesized their own version for their plan as well.
Gerald Robotnik from Sonic Adventure 2. The main conflict of the story is against Eggman, but it was Gerald's actions 50 years in the past that caused many of the problems in the game.
In the X series, it is discovered that The Virus that turns Reploids into Mavericks originated from Zero, and both were Wily's final creations before he died long before the X series. The Big Bad of the X series, Sigma, merges with the Maverick Virus and transforms it into the Sigma Virus.
In the Zero series that comes after the X series, Dr. Weil (no connection to Dr. Wily according to Word of God) creates Omega as a Dark Messiah to exterminate all Reploids. Omega's consciousness inhabits Zero's original body since Zero's mind was extracted after the X series. The Mother Elf, who becomes the Dark Elf, another major antagonist, was created by Ciel's ancestor by studying the Maverick Virus and trying to create an antibody.
In the ZX series, all the Biometals are created from studying the original Biometal Model W, created from the ruins of the Ragnarok satellite that Weil fused with at the end of Zero 4.
Orochi in Ōkami makes sure the yet-to-be-lifted evil curses cast by him wouldn't fade away after his defeat by Amaterasu and Susano. In addition, as his soul flies away to the north of Kamui to reactivate the Ark of Yamato to summon Yami, the Lord of Darkness, he releases several monsters originating from that place so they can terrorize all of Nippon, starting with Kamui itself.
Batman Beyond: The Joker might be dead, but his legacy (and the mysterious manner of his death) has resulted in roving gangs of criminals in various types of clown costumes and makeup all calling themselves "Jokerz" terrorising Gotham. Not that Old Bruce thought much of them.
Five hats means that five tropers think it is ready to publish.
You are saying that you think this draft is ready to be published. That means the description is not ambiguous,
it doesn't duplicate an existing trope, there are at least three examples, and the title makes sense.
Is that what you meant to do?
You are saying this draft has a ready-to-publish hat it does not deserve and you are taking it back.