Early career and Aston Villa Sarkic left the youth academy of Belgian club
Anderlecht, signing a three-year contract with English club
Aston Villa on 1 September 2015, joining their under-21 side. He was the
goalkeeper for Villa's under-21 team who reached the Premier League 2 Division Two play-off final in the 2015–16 season. In April 2017, he was named on the bench for a league match against
Reading as cover for
Sam Johnstone following an injury to
Mark Bunn. Šarkić joined
Wigan Athletic on 31 August 2017 on a season-long
loan, going on to make 3 appearances, all in cup competitions, and saving a penalty on his debut against Middlesbrough U21 in the
EFL Trophy. In December 2018, he joined
Stratford Town on a youth loan. On 26 June 2019, Sarkic signed for
Scottish Premiership club
Livingston on what was intended to be a season-long loan, but he was recalled by Aston Villa on 3 January 2020, as their first-choice goalkeeper
Tom Heaton had suffered a knee injury. Sarkic was offered a contract extension at Aston Villa in 2020 but turned down the offer to look for first-team opportunities elsewhere, having seen experienced goalkeeper
Pepe Reina brought in as cover for the injured Heaton. Sarkic was formally released by Aston Villa at the end of the 2019–20 season.
Wolverhampton Wanderers Sarkic signed for Villa's
Premier League rivals
Wolverhampton Wanderers on 27 July 2020 on a three-year contract.
Shrewsbury Town (loan) On 2 September 2020, Sarkic joined
League One club
Shrewsbury Town on a season-long loan. He made his debut on 12 September, starting in a goalless draw away at
Portsmouth. He kept 11
clean sheets in 29 games across all competitions for the Shrews before returning to Wolves on 6 May 2021; he had competed for a starting position against
Harry Burgoyne during his loan.
Birmingham City (loan) Sarkic joined
Championship club
Birmingham City on 26 July 2021 on loan for the season. With previous first-choice goalkeeper
Neil Etheridge still recovering from
COVID-19, Sarkic started the opening-day fixture away to
Sheffield United and kept a
clean sheet as Birmingham won 1–0. He retained his place in the starting eleven even after Etheridge's return to fitness, kept ten clean sheets, and missed only one of Birmingham's 24 league matches. Near the end of what proved to be his last appearance, on 2 January 2022, he dislocated a shoulder throwing the ball out to a defender. The injury required surgery which would keep him out for the rest of the season, and he returned to his parent club for treatment and rehabilitation. Despite only being at the club for the first half of the season, he was voted Birmingham City's Player of the Season for 2021–22.
Return to Wolves Although Wolverhampton Wanderers' goalkeeping coach,
Tony Roberts, thought Sarkic's progress would be better served by playing regularly on another loan, he signed a new three-year contract, and technical director
Scott Sellars said that he would remain at the club as backup and competition for
José Sá. He made his first-team debut on 23 August 2022, in the
EFL Cup second-round 2–1 win against
Preston North End.
Stoke City (loan) On 25 January 2023 Sarkic joined Championship club
Stoke City on loan for the remainder of the
2022–23 season. Sarkic took over from
Jack Bonham as first-choice keeper until he suffered injury against
Sunderland on 4 March 2023. He returned from his injury on the final day of the season at
Watford. In July 2023, Stoke agreed a fee with Wolves for Sarkic, however they were unable to agree personal terms so they decided to sign
Mark Travers instead.
Millwall Sarkic joined
Millwall on 3 August 2023 for an undisclosed fee. He made his debut on 5 August, starting in a 1–0 away win over
Middlesbrough. He made 33 appearances for Millwall during the
2023–24 season, as the team finished thirteenth in the
EFL Championship table. ==International career==