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 27th 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. There were more impressive performances over the next few weeks and he signed a new four year deal on 26th January 2023.