Adam Kleber was born in Chaska, Minnesota.
In 2020-2021, Kleber played for Chaska's U15 squad and scored nine goals and 44 assists in 40 games. In 2021-2022, Kleber played for the USHS Chaska team and in 28 games he tallied four goals and 13 assists.
He was selected by the Lincoln Stars of the USHL in 2022. In his first season he recorded eight assists in 56 games.
Last year he played the same amount of games for the Stars but was much more productive. He scored five goals and 21 assists, for an 18-point improvement.
Kleber is committed to play at Minnesota-Duluth in 2024-2025.