[3][4] He contributed to Viktoria Plzeň's 2023–24 UEFA Europa Conference League campaign, where they reached the quarter-final of a European competition for the first time.

On 26 January 2020, he was loaned to SK Dynamo České Budějovice in Czech First League.

In one year long loan he played in 15 league matches and scored 3 goals.

Šulc had played international football at youth levels that ranged from Czech Republic U18 to U21.

[citation needed] On 22 March 2024, Šulc debuted for the Czech senior squad in a friendly match against Norway.