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.
