People who are carriers for Blooms Syndrome have developed a selective advantage. How would this affect the allele frequency of the disease allele?
Natural selection will occur [..]
This is correct. Anytime you have a fitness differential among different genotypes, selection will affect allele frequencies.
[..] [l]eading to an imbalance of the hardy-weinburg equilibrium.
Hard-Weinberg equilibrium describes the relationships between allele frequencies and genotype frequencies. Selection can sure affect this relationship at some stage of life but it will not affect this relationship just after fecundation.
In any case, the question does not seem to expect you to talk about that. The question is asking about allele frequency only.
If you want to understand Hardy-Weinberg, you should definitely have a look at Solving Hardy Weinberg problems.
What I would answer
Not assuming any extra knowledge, the only simple, logic answer is to say that the frequency of the allele coding for the Blooms Syndrome will likely increase in frequency in the population, eventually reaching fixation. This increase in allele frequency would yield to an increase in the frequency of carriers of Blooms Syndrome.
Of course, if there is heterozygote advantage (aka. overdominance for fitness), then in an infinite population, the allele should never fully reach fixation.
If we were to know more about the genetics of the Blooms Syndrom or the specific selection advantage (and eventually many other things one may want to consider) one could formulate a more quantitative answer.