Linking Seniors to Needed Legal Services Act of 2021 This bill establishes a grant program within the Department of Health and Human Services for states to support linkages between health services, social services, and other supports for vulnerable older adults, including through senior legal hotlines and medical-legal partnerships. A medical-legal partnership means an arrangement in a health care or social services setting that integrates lawyers and social workers to address the needs of an individual patient related to social determinants of health (nonmedical factors such as income that influence health outcomes) and to help clinicians, case managers, and social workers address structural problems at the root of many health inequities.