Early career At 16 years old, Gauci caught the attention of scouts while captaining
West Torrens Birkalla's under-18s in the
National Premier Leagues (NPL). Gauci led his team to the title, triumphing over
Adelaide City in the final. After being released a year later, Gauci signed with Adelaide City mid-season of the
NPL South Australia in June 2019. He made eight league appearances in the
2019 season. On 9 September, Gauci signed a scholarship contract with
Melbourne City where he took part in the
club's youth teams. He was an unused substitute in the
2020 A-League Grand final defeat to
Sydney FC.
Adelaide United On 7 October 2020, Gauci signed a scholarship deal with his hometown club
Adelaide United. He kept his first
clean sheet in the league 15 days later in a 1–0 win over Sydney FC. The match was Adelaide's sixth consecutive win of the
2020–21 season, matching the club record in the
2005–06 season. Carl Veart, the head coach of Adelaide United, praised Gauci's performance during the team's success. On 13 May, Gauci suffered a thigh injury during a warm-up session before a match against Melbourne City, which ruled him out for the remainder of the season. He made ten league appearances during the 2020–21 season, keeping three clean sheets, and extended his contract for two years on 25 May. In the
2021–22 season, Gauci went seven-months without an appearance and was ruled out at the start of the new year with
COVID-19. He made his first appearance for the season, as to replace Delianov who sustained an injury mid-season, against Melbourne Victory on 8 January. In the
2022–23 season, Adelaide United progressed to the
A-League finals series. In the elimination final, Gauci kept his first clean sheet in 13 matches, in a 2–0 win over
Wellington Phoenix on 5 May. Adelaide United ended the season with a loss in the semi-final leg against Melbourne City. He was voted onto the
A-League Men PFA Team of the Season, having stopped 146 efforts on goal, including three penalties for a save percentage of 73%. In February 2024, midway through the
2023–24 season, Gauci departed Adelaide United with a total of 76 appearances and 16 clean sheets.
Aston Villa On 1 February 2024, Gauci signed for English
Premier League club
Aston Villa for an undisclosed fee. The fee was reported to be around $2.5m (around £1.29m). It was confirmed that the player would join up with his new club after the end of Australia's involvement in the
ongoing Asian Cup. Gauci was on the bench for the February 2024 game against
Nottingham Forest. The 24-year-old made his Aston Villa debut on 24 September 2024, starting an
EFL Cup win away at
Wycombe Wanderers.
Unai Emery had him compete with 34-year-old
Robin Olsen to be
Emiliano Martínez's backup. On 30 January 2025, Gauci joined
League One side
Barnsley on loan for the remainder of the season. Head coach
Darrell Clarke said the Australian would be Barnsley's first-choice goalkeeper. On 1 February, Gauci got a clean sheet in his first appearance in the
English Football League, a 0–0 draw with
Burton Albion at
Oakwell. However, he was sidelined with a hip injury after four games and 20-year-old
Kieren Flavell impressed new head coach
Conor Hourihane in his absence. Gauci played three further games for Barnsley in the remainder of the
2024–25 season. Manager
Darren Moore gave Gauci his debut at
Vale Park 12 days later, dropping number one
Marko Maroši to the bench for a 1–0 league defeat to
Doncaster Rovers. He was named on the League One Team of the Week for his performance in a 2–0 victory at
Exeter City on 13 September. Readers of the
The Valiant substack voted him as their Player of the Month for October. He continued to pick up good reviews, though Gauci acknowledged that he needed to improve his distribution skills. He spent a month on the bench before being restored to the starting line-up by new manager and fellow countryman
Jon Brady. On 14 April, he saved a penalty in a 0–0 draw with
Barnsley to help the Valiants to move off the bottom of the table for the first time in five months. The team went on to be relegated despite a strong defensive record in the
2025–26 season. ==International career==