Clean Competition Act This bill creates a carbon border adjustment mechanism to lower greenhouse gas emissions in high-polluting sectors. This mechanism imposes charges on imports from carbon-intensive (e.g., fossil fuels, refined petroleum products, petrochemicals) manufacturers, encourages decarbonization efforts, and funds future research, development, and deployment efforts to achieve a net-zero carbon future. The bill requires annual calculations of carbon intensity, imposes a carbon intensity charge on imports into the United States beginning after 2023, and allows for rebates for overpayments of charges. The bill also establishes a grant program in FY2025 and subsequent fiscal years for investments in new technology to reduce carbon intensity in existing facilities and ensure best-in-class carbon intensity for proposed facilities.