Career
Videoton
On 28 July 2013, he scored his first goal in the 2013–2014 season against Szombathelyi Haladás at the Sóstói Stadion, Székesfehérvár. The match ended with a 2–0 victory for Videoton Football Club. In the rest of the season he scored another three goals, one against Újpest Football Club at the Sóstói Stadion on 6 October 2013, one against Mezőkövesd-Zsóry Southeast in a 1–0 victory at the Sóstói Stadion on 8 November 2013, and the last goal against Diósgyőri VTK at the DVTK Stadion in a 2–2 draw match on 24 November 2013. In the 2014–2015 season, he played only 370 minutes in 11 appearances for Videoton Football Club and 911 minutes in 12 appearances for Puskás Akadémia Football Club. In July 2015, Kleinheisler refused to sign the extension of his contract with Videoton, therefore he was ousted to the reserves for the 2015–2016 season.
Videoton refused to sell him to the Ekstraklasa club Śląsk Wrocław in August.
Werder Bremen
On 20 January 2016, Kleinheisler joined Werder Bremen on a 3.5-year contract for an undisclosed fee. He made his debut in the Bundesliga on 30 January 2016 against Hertha Bachelor of Science in the Weserstadion.
He was brought onto the pitch in the 62nd minute at 0–2 to Berlin and helped Bremen come back from 0–2 and 1–3 deficits to earn a 3–3 draw. On 6 November 2015, Bernd Storck announced the squad for the Union of European Football Associations Euro 2016 qualifying play-off match against Norway.
The biggest surprise was the inclusion of Kleinheisler because he had not played a single match in the 2015-2016 Nemzeti Bajnokság I season.
Kleinheisler scored on his debut for the Hungarian national team in November 2015. His nickname is "Scholes", after Paul Scholes, because of the similarity of their hair.