He spent six years there before signing for Liverpool in 2017, joining the club's Academy set-up and winning the FA Youth Cup in his second season with the side.

[4] Jaroš first involvement with the Liverpool first team squad in a competitive fixture came in February 2020, when he was named on the bench for their FA Cup Fourth Round replay against Shrewsbury Town.

[7] On 3 February 2021, it was announced that Jaroš had joined League of Ireland Premier Division side St Patrick's Athletic on loan for the duration of the 2021 season.

"[11][12] He kept the first clean sheet of his senior career on 3 April 2021, as his side won 1–0 away to Bohemians in the Dublin City derby at Dalymount Park to go top of the league.

[39] He made 21 appearances in all competitions during his loan spell which concluded with winning the 2023–24 Austrian Bundesliga to complete the double and end Red Bull Salzburg's 10-year-long title-winning streak.

[40] On 5 October 2024, Jaroš made his Liverpool and Premier League debut, replacing Alisson in the 79th minute of a 1–0 away victory over Crystal Palace.

[41][42] He made his full debut for the club on 30 October 2024, starting in a 3–2 away win against Brighton & Hove Albion in the EFL Cup, earning praise for an incredible fingertip save onto the post from a Simon Adingra header in the 50th minute.

[49] Jaroš made his senior international debut on 7 June 2024 in a 7–1 friendly victory against Malta in Grödig, Austria, coming as a substitute for Matěj Kovář at half-time.