Eliminating Local News Deserts Act of 2021 This bill requires a cable company operating within a state to carry certain low-power stations under specified conditions. A cable company must carry such a low-power station if, among other requirements (1) the state has no exclusive, in-state broadcast television market within its boundaries; (2) there are no full-power commercial network affiliates (i.e., ABC, CBS, NBC, and FOX) that are licensed to, and principally operate within, the state; and (3) such low-power station provides a minimum amount of particularized local programming each week.