Born in Switzerland to ethnic Albanian parents (father from Tetovo and mother from Gostivar),[1][2][3] Bajrami spent all of his youth career with professional side Grasshoppers. He signed his first professional contract alongside teammates Petar Pušić and Arijan Qollaku in February 2017,[4] and made his debut the same month, playing the full 90 minutes of a 1–0 loss to FC Thun.[5]
Empoli
On 13 August 2019, Bajrami joined Italian Serie B club Empoli on loan with an option to buy.[6]
Sassuolo
On 31 January 2023, Bajrami moved to Sassuolo on loan with an obligation to buy.[7]
Rangers
On 30 August 2024, Bajrami joined Rangers in Scotland.[8] Bajrami scored his first Rangers goal in a 2-0 victory away at Malmö in matchday 1 of the UEFA Europa League on 26 September 2024. On 3 November 2024, Bajrami scored the winning goal in a 2-1 victory over Motherwell in the semi-final of the Scottish League Cup. On 15 December 2024, he scored Rangers opening goal in the League Cup final.
International career
Bajrami represented Switzerland in various youth sides up to under-21 level. He played for the Switzerland U17 team in their unsuccessful European Under-17 Championship qualification bid in 2016, featuring in all their six games.[9] He scored a total of five goals for the under-17 side, including a brace against Montenegro in 2015.[10] On 9 March 2021, Switzerland's U-21 manager Mauro Lustrinelli confirmed that Bajrami chose to switch allegiances and represent his country of origin, Albania.[11] Mauro stated “We tried to convince Bajrami to continue playing for Switzerland but he told us that his heart beats for Albania. For us in the national team, identification is one of the main values, so we had no choice but to let him leave.”[12]
In June 2024, Bajrami was called up to represent Albania at UEFA Euro 2024.[17] In their opening group stage match against defending champions Italy, Bajrami scored the fastest goal in UEFA European Championship history, only 23 seconds into the match, in an eventual 2–1 loss.[18]