How should bank capital requirements be set to deal with climate-related transition risks? We build a general equilibrium macro banking model where production requires fossil and low-carbon energy intermediate inputs, and the banking sector is subject to volatility risk linked to changes in energy prices. Introducing carbon taxes to reduce carbon emissions in fossil energy induces risk spillovers into the banking sector. Sectoral capital requirements can effectively address risks from energy-related exposures, benefiting household welfare and indirectly facilitating capital reallocation. Absent carbon taxes, implementing fossil penalizing capital requirements does not reduce emissions significantly and may threaten financial stability. During the transition, capital requirements can complement carbon tax policies, safeguarding financial stability and trading off long-run welfare gains at the expense of lower investment and credit supply in the short run.