We at Murthy Immigration Services receive calls regularly to confirm if one has to apply for a new visa when s/he has renewed her/his passport that has a valid U.S. visa. In most cases, one has to apply for a new passport if the previous one is expired or if there are no blank pages remaining in the passport.
We wish to clarify that a new visa is not required, and the visa holder should carry both their new and previous passport that has a valid visa while visiting the United States. The visa should be unmarked and undamaged, and the purpose of travel should be consistent with the valid visa. Additionally, the name and other personal data must be the same in both passports, and both passports must be from the same country and of the same type (i.e., both tourist passports or both diplomatic passports).
However, if the visa holder does not wish to carry two passports while traveling to the United States, s/he may renew her/his visa through the interview waiver program / dropbox program. One must remember that while doing so, it will be treated as a new application and the consular officer, at her/his discretion, may require the applicant to appear for a personal interview. If all requirements are met, a new visa will be issued.