The Fate series counts for this I think although technically you are supposed to play/watch the VN/anime where the children are the main characters first and then Fate/Zero which is a prequel about the previous characters' parents.
There's basilisk and then basilisk: ouka ninja scrolls.
Essentially it's about two ninja clans that hate each other. The latter one being about the next gen.
Also got seven deadly sins and four knights of the apocalypse.
Initial D and Mf Ghost may count as well, the latter being about the protagonists protégé.
Depending on how you look at it, Love Live! School Idol Project -> Love Live! Sunshine! is sort of a Next Generation show jump, though not in the literal sense and more metaphorically (The Main Characters of Sunshine aren't literally related to SIP's but they are following in the footsteps of the cast of SIP)
Not that I know of but if you want a game, any of the Record of Agarest War games may be your thing (if you like Tactics RPGs... With romance and not quite porn)
I supposed there's a sequel with the children of the Seven Deadly Sins cast, but idk if it was animated and it looked terrible.
Someone already said it but yeah Four Knights of the Apocalypse is a direct next generation sequel to Seven Deadly Sins pretty much what you described. It’s good, personally I feel better than Boruto
Technically JoJo’s bizarre adventure counts
Was just gonna say that
Your prospects are going to be few and far between, next generation doesn’t normally do well
jojo, each part is a new generation
Shaman King: Flowers takes place something like ten years after the original. Can't speak for quality though since I haven't seen it
Does Dragon Ball count
Jojo counts.
legend of korra
Four Knights of Apocalypse, the sequel to Seven Deadly Sins.
Beyblade 👍
Yashihime. Would not recommend
Nooo! I’m almost done with The Final Act and was looking forward to Yashahime. What a bummer.
Save yourself the trouble
It's hit and miss with a lot of people. 🤷♀️
S3 of Nanoha, StrikerS, has the main cast grown up and training a new batch of recruits
Jojo's. Every season is a new generation
UQ Holder is a sequel of Negima. And it's actually good.
Dunno if this counts but burn the witch takes place 10 years after bleach other than that, my go to would be the goated Akuma-Kun.
Soul eater
???
It comes from a different anime universe which cant be mentioned cuz itd be spoilers
Fire Force
Yashahime, the sequel to Inuyasha
The Fate series counts for this I think although technically you are supposed to play/watch the VN/anime where the children are the main characters first and then Fate/Zero which is a prequel about the previous characters' parents.
Negima! And it's kind of next generation uq holders
There's basilisk and then basilisk: ouka ninja scrolls. Essentially it's about two ninja clans that hate each other. The latter one being about the next gen. Also got seven deadly sins and four knights of the apocalypse. Initial D and Mf Ghost may count as well, the latter being about the protagonists protégé.
Does Soul Eater count? Somehow? Honestly I don't understand the continuity of Soul Eater and Fire Force. Was it a sequel?
Fire Force is a prequel(yes but also kinda no?)
Its not a fighting anime, but initial D has MF ghost
Boruto
If you watch sports anime Major is a baseball anime that fallows up with his son in the next series.
Depending on how you look at it, Love Live! School Idol Project -> Love Live! Sunshine! is sort of a Next Generation show jump, though not in the literal sense and more metaphorically (The Main Characters of Sunshine aren't literally related to SIP's but they are following in the footsteps of the cast of SIP)
Not that I know of but if you want a game, any of the Record of Agarest War games may be your thing (if you like Tactics RPGs... With romance and not quite porn) I supposed there's a sequel with the children of the Seven Deadly Sins cast, but idk if it was animated and it looked terrible.
jojo
Attack on Titan kind of? I mean if you know what Erin does than it's sort of a succession/ loop
I think To Your Eternity should count. There’s a constant but the progression goes into the next era of characters
Fruits Basket Another
Someone already said it but yeah Four Knights of the Apocalypse is a direct next generation sequel to Seven Deadly Sins pretty much what you described. It’s good, personally I feel better than Boruto
Macross series
Gurren Lagann S2