Bajcetic arrived as a centre-back from Celta Vigo's youth team but soon started to forge ahead as a defensive midfielder. He signed a new contract in the 2022/23 pre-season after impressing the Liverpool coaching team in the first-team's warm up games. “He has amazing physical characteristics. He is extremely quick, makes good recoveries, has a great spring, is really impressive in the air and carries the ball cleanly out of defence,” Alex Otero, youth football co-ordinator at Celta, told The Athletic in January 2021. “It was clear he was a standout player in his age group. He can really play and help construct attacks but he is also noticeable for his comfort with his left and right foot and the ability to play on the right or left of the centre-backs. That is quite rare."

Still two months short of his 18th birthday, Bajcetic made his first team debut on 27 August 2022, coming off the bench to play the last twenty minutes of a 9-0 win over Bournemouth. He made three substitute appearances in the Champions League group stages and scored his first goal for the club when he came off the bench in a 3-1 win over Aston Villa on Boxing Day. Bajcetic's rise at Liverpool has been rapid in the troubled 2022/23 season and he was rewarded with a new contract in January 2023. Throughout 2023/24 Bajcetic struggled with a calf injury and was limited to just three appearances, two of them in the Europa League. His one Premier League appearance was as a 65th minute substitute at home to Tottenham on 5th May. Bajcetic's lack of sharpness showed and the Reds won 4-2, it had been 4-0 when he came on. Jurgen Klopp admitting is was a mistake to rush the promising teenager back, saying: "He comes on and it’s like you arrive on the motorway with your bicycle."

Bajcetic was loaned to Red Bull Salzburg for the 2024/25 season, where Pep Lijnders, his former coach at Liverpool was manager. Things didn't work out as planned, with Lijnders being sacked halfway through the season and after making eight starts and eleven substitute appearances, he was recalled in January and loaned to Las Palmas, who were battling relegation from La Liga. Although he was unable to save the Canary Islanders from the drop, he got far more game time and was praised for some battling performances. A serious hamstring injury suffered near the end of the campaign required surgery, and setbacks during his rehabilitation prevented him from playing throughout the entire 2025/26 season. Although he eventually returned to training, he was unable to force his way back into Liverpool’s plans.

Bajcetic completed a permanent return to his former club Celta Vigo in August 2026, ending a five-and-a-half-year association with Liverpool. He left with a record of 22 senior appearances and one goal. His early performances had suggested that he could become an important part of Liverpool’s midfield for years to come, but injuries repeatedly interrupted his development. Still only 21 when he departed, the move back to Vigo offered him an opportunity to rebuild his fitness and revive a career that had shown such considerable promise at Anfield.