Elmas was born in Macedonia to a family of Turkish descent. In July 2017 it was reported the coach of the Turkey national football team, Fatih Terim, had tried to call him up, but Elmas decided to represent his birth country.

On 11 June 2017, at the age of 17, Elmas made his debut for the Macedonia national team in a FIFA World Cup qualifier against Spain by coming in at halftime as a substitute for Ostoja Stjepanović.

Elmas started his career at FK Rabotnički in his native Macedonia. After a stand-out season in which he scored 6 leagues goals and lead Rabotnički to a third place finish in the Macedonian First Football League in 2016–17, he joined Turkish giants Fenerbahçe on a deal until 2022, with Fenerbahçe paying the former €300,000 for his services. The attacking midfielder went onto score four goals in over 40 appearances for the Yellow Canaries in all competitions before moving to Italy in July 2019.

On 24 July 2019, Serie A side S.S.C. Napoli announced the signing of Elmas from Fenerbahçe. The deal was worth a reported €16m, which could rise to €19m in total with bonuses – including a €1.5m sell-on fee clause. He was disciplined by his new club after speaking to reporters while away on international duty in November 2019 for breaching a club media blackout.

Elmas scored his first Napoli goal on 3 February 2020 to help the club to a 4–2 victory over Sampdoria, and secure their third win in a row in all competitions.