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 2 appearances in the Austrian Cup in which they won. He made 5 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 2 points. He scored his first goal in football in the 2010–11 season. Suttner won his first Austrian cap whilst at the club in 2012. Suttner played in 35 league games, scoring 3 in the 2012–13 campaign where Austria Wien won the league title for the first time in 7 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.
Suttner signed for newly promoted FC Ingolstadt 04in 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 4 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 2 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 3 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 3 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 the 18 January 2019 who were playing their first season in the German top flight since the 2012–13 Bundesliga. He made his debut on 6 February in a DFB Pokal match where he started and played the full match in the 4–1 away defeat to Schalke 04. The next game he played in was a league game away against Bayer Leverkusen where Fortuna lost 2–0 on the 17 February. On 27 April Suttner scored against SV 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
Suttner made seven appearances for Austria's Under-21 side, before making his full debut on 1 June 2012, in the 3–2 win over Ukraine in a friendly match. Suttner was a part of the squad for the UEFA Euro 2016 but did not make an appearance in any of the three games where Austria finished bottom of their group. After 20 caps, it was announced on 10 May 2017, that he had retired from international football.
