[3] Klein has reached 15 career singles finals, with a record of 9 wins and 6 losses, including 3 ATP Challenger titles.

Klein won the doubles title at the 2021 Challenger La Manche with compatriot Alex Molčan 1–6, 7–5, [10–6].

He would go on to lose in the second round to top seed, local favourite and eventual champion Diego Schwartzman in straight sets.

248 in singles on 28 June 2021 after reaching the second round also as a qualifier at the 2021 Mallorca Championships by defeating 8th seed Dušan Lajović, for his second ATP win for the season and in his career.

In January 2024, he qualified for the 2024 Brisbane International and defeated sixth seed Sebastián Báez for his first ATP win of the season and only third in his career.

163, he qualified for the 2024 Australian Open making his debut at this tournament and recorded his first Major win over Kwon Soon-woo.

[9] He qualified for the 2024 BNP Paribas Open making his Masters debut and recorded his first win at this level over Nicolas Moreno de Alboran.