He currently plays for Slavia Praha U19, wearing the number 22 shirt. He plays primarily as a Midfield. His current market value is estimated at 250K €.

His most recent move was a from SK Slavia Prague U20 to Slavia Praha B on 2025-12-31.

Across 4 appearances in the UEFA Youth League 2025-2026, Martin Palaščák registered 0 goals and 0 assists, while completing 0 key passes out of 60 total passes with a passing accuracy of 10.5.