At least three of the spike mutations, N501Y, N439K and Y453F, may help the virus to infect human cells. These, and another change in the spike called delta69/70, might help the virus evade antibodies from people who have caught the virus before or had a vaccine shot.
It is unlikely that the new variant will evade antibodies from people who were infected in the past. In our lab we test for both nucleocapsid-based and spike-based antibodies and most subjects develop both N-based and S-based antibodies. Less than 10% of people develop a pure S-based immunity. Hopefully the N protein is known to be less prone to mutations than the 2 S subunits. This is one reason why some manufacturers (e.g. Roche, Epitope Dx) developed a test that targets the N-based antibodies. Only a very few tests target both N and S and it is not surprising that it is those tests that have the best sensitivity.
Unfortunately the same does not apply to vaccines. Most vaccines are S-based. AFAIK this is the case for the mRNA vaccines of Pfizer and Moderna for which new variants may evade the antibodies developed after vaccination. I heard that they are already working on a new form of the vaccine. Repeat vaccination is good for business....