[4][5] Bajcetic was a member of the Celta Vigo youth academy, and signed for Premier League club Liverpool in December 2020 for £224,000.

[13] On 9 November 2022, Bajcetic started his first game for Liverpool, in a home win against Derby County in the third round of the 2022–23 EFL Cup.

[17] On the field, he continued to progress, starting three consecutive Premier League games against Chelsea, Wolverhampton Wanderers, and local rivals Everton.

[18] On 21 February, he became the youngest Liverpool player, aged 18 years and 122 days, to start in a Champions League knockout match, which ended in a 5–2 home defeat against Real Madrid.

[22] After making 19 appearnces for Salzburg, including 12 in the Austrian Bundesliga on 31 January 2025, Bajcetic moved on to an new loan to Las Palmas in La Liga.