Avenging the Villain

If the heroes have defeated a Big Bad or Evil Overlord, there is a chance that they have an offspring, daughter/son or maybe just an apprentice who will come back to menace them in the sequel or next season.

This isn't a trope that would be used for villains who only care about themselves, and it's pretty rare in one who'd bother becoming the Big Bad, because it shows the villains had loved ones or people they cared about.

In most cases, the villain's brother/sister/etc. won't actually care about the deceased villain and may or may not be out for the hero's blood for other reasons.

In fact, subversions are more common than straight examples. If the character in question realises that the slaying was accidental or justified, they might settle for Restrained Revenge.

Sometimes results in Nice Job Breaking It, Hero!, if the new enemy is even more powerful than the former.

Examples

 * The bad guys in The Lion King II: Simba's Pride are a faction of lions who pledged allegiance to the now-dead Scar and were banished by Simba. Scar's former mate Zira is trying to raise her son Kovu up to kill Simba for killing Scar and become the new king. Never mind that the hyenas were the ones to kill Scar.
 * The Little Mermaid II: Return to the Sea: Morgana initially claims she's coming after Ariel and Eric to avenge the death of her sister Ursula. It's ultimately subverted; in reality, Morgana always hated Ursula for being their mother's favorite and wants to prove herself better.
 * The plot of The Dark Knight Rises is because Bruce "let Ducard/Ra's die" in Batman Begins. Bane and Talia, who used to have a rather strained relationship with her father prior to that, then seeks to accomplish her father's visions.
 * A hallucination of Norman Osborn rather strongly insisted upon this in Spider-Man 2.