Fair, Affordable, Innovative, and Resilient Transition and Competition Act or the FAIR Transition and Competition Act This bill requires the Department of the Treasury, not later than July 1, 2023, and annually thereafter, to determine the domestic environmental cost incurred for industrial facilities producing steel, aluminum, cement, iron, or other products (sectors), and for the production of natural gas, petroleum, or coal (covered fuels) that are or may be used to emit greenhouse gases. By that same date, the Environmental Protection Agency must determine and publish the average greenhouse gas emissions of each sector to determine progress in reducing such emissions. The bill imposes a fee (border carbon adjustment) on importers of covered fuels and products. Treasury must provide to each state a resilient communities grant to provide job training and worker transition assistance, assist certain governmental entities and frontline communities, alleviate historical burdens imposed on communities of color and other vulnerable populations, and to assist small businesses disproportionately impacted by the border carbon adjustment fee.