Climate Solutions Act of 2021 This bill establishes renewable energy standards, energy saving targets, and greenhouse gas emission reduction targets. Specifically, the Department of Energy (DOE) must promulgate regulations to increase the percentage of electricity sold in the United States that is generated from renewable sources. By 2035, 100% of electricity must be generated from renewable sources. DOE must also promulgate regulations that set end-user electricity savings targets for retail electric energy suppliers and natural gas saving targets for retail natural gas suppliers through 2030 as specified by the bill. Each year's savings must be in addition to the previous years' savings. DOE must allow suppliers to achieve the targets through a market-based trading system. The Environmental Protection Agency (EPA) must promulgate annual net emission reduction targets from 2030 through 2050 to ensure that U.S. greenhouse gas emissions (1) in 2035 are at least 52% below those in 2005, and (2) in 2050 are zero. The EPA must promulgate final regulations to implement those targets within seven years and review them at least every five years thereafter.