The multi-million pound building, which will include a theatre, rehearsal studios, production workshops and an amphitheatre, was due to be completed later this year.
But construction was halted when contractor Clugston fell into administration earlier this year, and has been further delayed by the coronavirus pandemic.
In the meantime, the college have secured 'unprecedented' use of Unity House, a former office building in the city centre.
Claire Nicholson, Principal of CAPA College, said: "We are so excited about what will be able to offer from our new extended base at Unity House.
"It is paramount to the ethos of CAPA College that our students have access to the best teaching, facilities and experiences as we look to inspire and train the next generation of performers, creatives, designers and technicians.
"But we are also thrilled to now be in a position to share some of the magic of CAPA College with the wider community.
"We hope that CAPA College will become another hub for artistic talent in the North of England."
Like many other schools and colleges, CAPA faced uncertainty during the lockdown, and was forced to quickly adapt to distance learning.
After loaning laptops to students on a long-term basis, the college launched a full remote timetable, with live-streamed classes in dance, drama, singing and more.
Staff hope to begin resuming face-to-face classes for some students from next week.
Once complete, the CAPA College building on Mulberry Way will provide facilities for up to 500 students, and hopes to become a flagship provider of performing arts education in the North of England.
The college offers training in Performing Arts, Dance, Drama and Production Arts and Media, and hopes to introduce a range of public classes, workshops and projects once the new site is up and running.