[3] Since 2006, he has been the deputy chairman of the board of the joint-stock company Sompo, which provides comprehensive services in the field of waste management.

[4] Vlček has also been a member of the board of directors of the Pevak Pelhřimov cooperative since 2006, which deals with the sale of water and the management and maintenance of waterworks facilities.

[19][20] In the 2021 Czech parliamentary election, Vlček ran as a member of the STAN movement in second place among the candidates of the Pirates and Mayors coalition in the Vysočina Region.

[23] In the 2022 municipal elections, he ran for the council of Pacov from the second place as STAN candidate and defended the mandate of town representative again.

[26] Shortly before taking office, Vlček stated that he considered the Greens Party agreement for Europe to be an opportunity for the Czech Republic.