Indigenous Peoples are increasingly exerting governance and oversight over genomic research with citizens of their nations, raising questions about how best to enforce research regulation between American Indian, Alaska Native, and Native Hawaiian peoples and researchers. Using a community-engaged research approach, we conducted 42 semi-structured interviews with Tribal leaders, clinicians, researchers, policy makers, and Tribal research review board members about their perspectives on ethical issues related to genetics research with Indigenous Peoples in the US. We report findings related to 1) considerations for Indigenous governance, 2) institutional relationship upholding sovereignty, 3) expectations for research approvals, and 4) agreements enacting Indigenous governance. Participants described concerns about different ways of exerting oversight, relationships and agreements between Indigenous Peoples and researchers, and gaps that need to be addressed to strengthen existing governance of genomic data. The results will ultimately guide policy-making and development of new strategies for Indigenous Peoples to enforce oversight in research to promote ethically and culturally appropriate research.