Polar Bear Seas Protection Act - Amends the Outer Continental Shelf Lands Act to prohibit the Secretary of the Interior from offering or approving any new lease, or approving an exploration or development plan, within any area of the Chukchi or Beaufort Sea marine and coastal ecosystems until: (1) the National Research Council reports to Congress on certain missing information regarding the composition, distribution, status, and ecology of the living marine resources in such ecosystems; (2) the polar bear is listed as either an endangered or threatened species under the Endangered Species Act of 1973 and critical habitat is designated for it; (3) the Secretary performs an oil spill response gap analysis for proposed and existing arctic oil operations; and (4) the Secretary makes specified determinations, including that oil and gas exploration and development can be conducted in the Beaufort and Chukchi Sea Planning Areas without posing a risk of substantial adverse impact to wildlife, or wildlife habitat and subsistence.