Šulc is part of the first team of Viktoria Plzeň since 1 January 2020. He played his first match for this team on 17 January 2021 against 1. FK Příbram.[citation needed]
On 3 July 2019, he was loaned to SFC Opava in Czech First League. In six months long loan he played in 15 league matches and in 1 Czech Cup match without scoring a goal.
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.
On 21 June 2022, he was loaned to FK Jablonec in Czech First League.
International career
Šulc had played international football at youth levels that ranged from Czech Republic U18 to U21. He played in 19 matches and scored five times.[citation needed]
^Petr, Tomáš (27 March 2024). "Máme lavičku, která fandí, chválí Hašek atmosféru v celém týmu. Rozhodování o Euru bude složité". Czech Radio (in Czech). Proti Arménii si premiérový start v reprezentaci připsali kromě Vlčka ještě další čtyři hráči. Navíc už v pátek v Norsku debutoval Pavel Šulc. Z aktuálního kádru se nedostalo jen na brankáře Vítězslava Jaroše. [Apart from Vlček, four other footballers also debuted in the national team against Armenia. Pavel Šulc also made his debut in Norway on Friday [22 March]. Only goalkeeper Vítězslav Jaroš was not selected from the current squad.]