Climate-related transition risks are expected to escalate in the coming years, posing potentially significant threats to the banking system. This paper employs a DSGE model that incorporates heterogeneous firms and financial frictions to demonstrate the need to explicitly address climate-related risks in the prudential framework. Our findings indicate that failing to acknowledge transition risk can lead to excessive risk-taking by banks, thereby increasing the volatility of lending and output. With the introduction of climate-related prudential policies, banks are less exposed to transition risk and more efficient in allocating capital.