High Risk Rural Roads Safety Act of 2021 This bill establishes a high-risk rural roads safety program to support safety improvements for roads in rural and tribal communities. Specifically, the bill directs Department of Transportation (DOT) to provide grants to Indian tribes to improve safety on high risk rural roads. It also requires DOT to set aside specified funds for Indian tribes and states. Funds apportioned to a state must be obligated in areas of the state in which the population is not more than 50,000. The federal share of the cost of a project carried out under the bill may be up to 100%.