Answer to this depends upon the mechanism of action and genetic structure of the vaccine in use. For instance , a vaccine whose construct is inactivated form of whole virus will generate an immune response that will have more probability** to deal with the mutated forms. While a vaccine based on mimicking the outer spike protein and then generating an immune response , will be more susceptible to fail against mutated form. Although the choice of vaccine to be taken is based on personal preferences, beliefs, efficacy data, the mechanism of action and type of construct is a factor to llok out for.
From what we know about the new variant B.1.1.7 , it is not more infectious on paper as of now, so being optimistic the current vaccines would be effective.
* *The reason for a probability term is the failure of any vaccine to escape mutants.
So far we have some vaccine options that target the Spike protein on the surface of virus and new variant of virus has only mutations which resulted in 9 different amino acids in comparison to the wild type. Between around 2000 amino acids in the whole Spike protein these 9 amino acids are not too much and fortunately does not show any impact on produced neutralizing antibody. Hope it would be of help.
The coronavirus vaccines currently on the market should still work against new, more infectious variants discovered in recent months, although they may not be as effective, https://www.cnbc.com/2021/01/19/bidens-new-cdc-director-says-shes-optimistic-covid-vaccines-will-work-against-new-variants.html
Pfizer found that antibody-rich blood serum samples from 16 vaccinated people showed that vaccine was equally as effective at blocking the British variant as it was against the original version of the virus that took hold in Wuhan, China, a year ago. https://www.washingtonpost.com/health/2021/01/25/covid-vaccine-virus-variant/
Pfizer and Moderna: COVID-19 vaccines protect against new strains. https://www.news10.com/news/pfizer-and-moderna-covid-19-vaccines-protect-against-new-strains/