Jeltsch started his playing career with SV Raitersaich before joining
1. FC Nürnberg in 2015. On 18 February 2024, the
U-17 European and
World Champion made his professional debut for Nürnberg in the
2. Bundesliga, coming on as a half-time substitute during a 1–1 against
1. FC Kaiserslautern. In June 2024, he signed a new long-term contract with the club. On 3 February 2025, Jeltsch signed a five-and-a-half-year contract with
VfB Stuttgart until June 2030. He made his
Bundesliga debut on 15 February, coming on as a substitute in a 2–1 loss to
Wolfsburg. Ever since, the talented
centre-back has become part of the starting line-up in the majority of Stuttgart's matches, e.g. by starting against
Bayern Munich in a 3–1 away loss; although he was praised for his performances by
his coach. On 2 April, he played full 90 minutes and a crucial role in the
DFB-Pokal semi-final, a 3–1 victory over
RB Leipzig, helping his team advance to the
final for the
first time in 12 years. Fabian Wohlgemuth,
CEO of sports at VfB Stuttgart, praised the 18-year old for his performances: "He's currently a regular at the back. He's stabilized even further over the past few weeks and has become an important factor in our defense." Jeltsch would play in the
final and help his side win the DFB-Pokal and thus their first title in 18 years. ==International career==