Austria Wien Suttner came through the youth system at
Austria Wien before making his breakthrough season at the
Viennan club in his first professional season, in the 2008–09 season where he made 22 league appearances. He also made two appearances in the
Austrian Cup in which they won. He made five appearances in the
Europa League in 2009 where Wien qualified through the third round and the play off round but finished bottom of the group finishing with two points. He scored his first goal in football in the 2010–11 season. Suttner won his first
Austria national team cap whilst at the club in 2012. Suttner played in 35 league games, scoring three in the
2012–13 campaign where Austria Wien won the league title for the first time in seven years. Wien were to compete in the
Champions League in the 2013–14 campaign after being crowned champions of the Austrian league in previous season. They managed to qualify to the group stages from the third round of qualifying. However, they finished bottom of their group. Suttner played in one more season for the club where they finished 7th before moving to Germany.
FC Ingolstadt 04 Suttner signed for newly promoted
FC Ingolstadt 04 in the summer of 2015. In his first season he made 18 league appearances as the team finished 11th in the table. Suttner scored his first German
Bundesliga goal in the 2016–17 season where he finished with four goals to his name in 31 appearances. However, the season ended in relegation for the
Bavarian side.
Brighton & Hove Albion On 13 July 2017, Suttner signed for another newly promoted side,
Brighton & Hove Albion of the
Premier League. Just 12 days beforehand his Ingolstadt teammate
Pascal Gross signed for the Sussex club. Suttner made his debut for Brighton on 12 August 2017 in the opening game of the season at home to
Manchester City in which The Seagulls lost 2–0 to the eventual champions. He played in the following game in another 2–0 scoreline, this time in an away defeat to
Leicester City. Suttner played in Brighton's first ever win in the Premier League in a 3–1 home win over
West Brom on 9 September 2017 in which Pascal Gross scored two with
Tomer Hemed netting the other. Suttner made his
FA Cup debut in a 1–0 away win over
Middlesbrough with
Glenn Murray scoring a 90th-minute winner. Suttner played in three FA Cup matches where they were eventually knocked out by
Manchester United in the Quarter Finals. Brighton finished the season in 15th place securing safety in a 1–0 home win over Manchester United on 4 May 2018 where Gross scored a header that only just crossed the line from a
José Izquierdo cross. Suttner was absent from this match squad however. In his first season at Brighton he played 14 Premier League matches and three FA Cup matches. Suttner played in his first
EFL Cup match on 28 August 2018 in a 1–0 home defeat against south coast rivals,
Southampton. This turned out to be his only appearance for the Sussex club this season being sent out on loan in January 2019.
Loan to Fortuna Düsseldorf Suttner signed for
Fortuna Düsseldorf on loan on 18 January 2019 who were playing their first season in the German top flight since the
2012–13 Bundesliga. The next game he played in was a league game away against
Bayer Leverkusen where Fortuna lost 2–0 on 17 February. On 27 April Suttner scored against
Werder Bremen to make it 4–1 and to seal the win.
Fortuna Düsseldorf On 30 July 2019, Suttner joined
Fortuna Düsseldorf on a year-long contract. ==International career==