Upvote:4
Yes, and in fact they must:
If you obtain a new passport or change your name, gender or country of citizenship, you will be required to apply for a new travel authorization. This is also required if one of your answers to any of the VWP eligibility questions changes. The associated fee of $14 will be charged for each new application.
Alternatively, if they have a new passport for the country that granted them the visa previously, they can just bring both passports because the old visa continues to be valid.