Born in Revúca, Gyömbér started playing football with club , before moving to the youth team of Corgoň Liga club FK Dukla Banská Bystrica in 2006. Norbert made his professional debut with Dukla Banská Bystrica on 1 October 2011 in a league match against MFK Ružomberok. On 25 May 2012, Gyömbér was voted by Dukla Banská Bystrica's fans as player of the season, despite starting in just 18 league matches. He was also named Revelation of the 2011–12 Corgoň Liga's season in July 2012, after his successful first season with FK Dukla Banská Bystrica.
Catania
Calcio Catania officially agreed to the permanent transfer of midfielder Norbert Gyömbér from Dukla Banská Bystrica during the 2013 January transfer window, though the transfer was not officially be completed until 1 July 2013. The 20-year-old signed a 4.5-year deal at the Stadio Angelo Massimino, but finished the 2012–13 season with the top-flight Slovakian side.
On 15 August 2016, Gyömbér joined Pescara on a season-long loan. He first appeared in a Cup match against Frosinone in August, however, after only 5 games, he fractured his tibula in a 49th minute of a match against Lazio Romain September. Although between December 2016 and February 2017 he appeared in 6 of Pescara's 10 matches, rumours have surfaced about disagreements with some of his teammates and consequently, he was removed from the squad by club's disciplinary action in mid-February. However, according to Gyömbér, this rumour was "not true at all" and the real cause were disagreements with the coach of Pescara at the time, Massimo Oddo, who shortly after replaced by Zdeněk Zeman after a series of unsuccessful results, which Gyömbér claims to be one of the reasons for tensions. He revealed these claims in an interview on 21 March 2017, in a national team camp in Senec, prior to the FIFA World Cup qualifier against Malta.
On 14 August 2018, he signed a three-year contract with Serie B club Perugia.
International career
Gyömbér was selected in Slovakia's squad for UEFA Euro 2016, making two appearances as Slovakia reached the round of 16.
Ján Kozák's resignation incident
Gyömbér was nominated for a double fixture against Czech Republic and Sweden on 13 October and 16 October 2018, respectively. He did not play in either of the two matches, but was involved in the controversy, that had led to resignation of Ján Kozák, then Slovakia's longest serving and most successful coach, who introduced him to the national team. Gyömbér violated the code of conduct of national team player, along with Martin Dúbravka, Michal Šulla, Ľubomír Šatka, Milan Škriniar, Vladimír Weiss and Stanislav Lobotka. On the night of 13 October 2018, after loss in Slovakia's second UEFA Nations League fixture and a derby match against Czech Republic, they left the hotel and went out, missed the bedtime and violated the wellness policy, regarding regeneration and rehabilitation. They were allegedly busted by Ján Kozák at about midnight, admitting to the incident and apologising during the next day. Ján Kozák resigned from the national team in afternoon hours of 14 October, revealing the details of his decision in a press conference on 18 October, to avoid distractions during the preparation for the fixture against Sweden, that was managed by his former assistant Štefan Tarkovič on a caretaker basis. Kozák cited his inability to work with the squad under such conditions as the primary reason, as about a third of the squad was involved. President of SFZ, Ján Kováčik, said that the players will be punished by not receiving any financial rewards for any future nominations and performances in the national team during the upcoming qualification cycle. On 19 October, SFZ published statements of Gyömbér and other trespassers. His statement was the briefest, expressing that he was sorry for the misconduct, preparedness for the disciplinary sanctions and the fact that it was not aimed or intended to challenge Kozák. Nonetheless, Gyömbér was the only trespasser, who claimed that the events, as presented by the media, didn't match the reality.
After the arrival of the Czech-native Pavel Hapal, Gyömbér lost his spot in the national team, as early as November 2018, failing to regain it in March 2019. He managed to make a national team come-back in October 2019 for a qualifier against Wales, when it was required to fill the role of a second center back, as Denis Vavro had suffered a yellow card suspension. He played for the national team after over a year and his gameplay was seen generally positively, mainly for his uncompromising play, as he was tackled harshly on numerous occasions. His gameplay, however, caused him to be sanctioned with two yellow cards.
