Total human-caused mortality (including legal harvest, human-bear conflicts, and polar bears killed as a result of other human activities, etc.) does not currently threaten the persistence of polar bears at the circumpolar level. Such removals could, however, become a threat to individual subpopulations if legal take is unregulated or is not sustainable.
Source: Circumpolar Action Plan
Further reading on the IUCN Polar Bear Specialist Group website