Klimowicz trained with
Borussia Dortmund's academy at a young age, while his father was playing in Germany. He later joined
Instituto's ranks. He appeared professionally twice at the back end of the
2016–17 season in
Primera B Nacional, participating in fixtures with
Juventud Unida, aged sixteen, and
Nueva Chicago as they secured sixth. Klimowicz's first senior goal arrived on 14 October 2017 during a 1–1 home draw with
Aldosivi. On 10 May 2019,
VfB Stuttgart announced the signing of Klimowicz ahead of the
2019–20 season; with the midfielder signing a five-year contract. He made his bow as a late substitute in a
2. Bundesliga match with
1. FC Heidenheim on 4 August. On 1 September 2022, Klimowicz signed with
2. Bundesliga club
Arminia Bielefeld on a season long loan. ==International career==