You would never be able transplant the brain, and it’s still subject to the mutations and telomeres. The only way would be to transplant the personality Altered Carbon style or completely cure brain cancer.
IIRC, telomeres are essentially the self-destruct button for DNA. They get shorter everytime DNA replicates and when they are all used up, DNA stops replicating and the cell destroys itself. The telomeres help prevent too many mutations from building up or cancer from forming.
They was some research on animals that indicates that resetting the telomeres can extend the lifespan of the animal. But, without the telomeres, cancer and mutations eventually kill the organism.