Foundation is an Asimov book series, it follows almost exactly the same structure you described where it follows a group of characters up to some major event, then skips forward decades or centuries to another group with some relation to the previous ones.
Nora Starling
Nora blinked and rubbed her eyes. She sat up, groaning at the strange pains in her back and neck—the consequence of falling asleep on the couch. In front of her, the TV was still running, though she didn’t know exactly what the hell she was looking at. The last thing she...
"Three down is when I feel the rush. It’s intoxicating."
Name: Nora Starling
Gender: Female
Age: 19
Trainer Class: Champion (Hoenn)
First Pokemon: Surskit
Overview:
The young champion of the Hoenn league whose arrival in the professional scene came swiftly and unexpectedly. She is...
Eva Zapalac
Eva wandered about the club fair aimlessly as usual. She’d been here many times before, and yet had never actually gotten engaged in any clubs. It just wasn’t really her style. She couldn’t battle or coordinate terribly well, and her Magneton never really showed much interest—or...
Eva Zapalac
“Eh, makes sense,” Eva replied once Alto addressed her. She turned away, one elbow on the stand, and briefly glanced at her wrist as if she were checking the time. It was a habit of unknown origin, since she'd never worn a watch, indeed rarely checked the time at all. Meanwhile, her...
Eva Zapalac
“Here it comes!” were the words that rang out in Eva’s head as the song blaring through her headphones approached its climax. She could acutely feel the vibrations through her drumsticks as she tried her hardest to resist the temptation of speeding up the tempo to match her...
Name: Eva Zapalac
Age: 17
Team: Ignite
Gender: Female
Hometown: Nimbasa City, Unova
Career Path: Music
Appearance (from Picrew, credits in watermark):
Background:
In Eva’s childhood, her father often described her as the Sun. This was chiefly due to her seemingly endless supply of energy, which...