Access to finance is a major barrier to clean innovation. We incorporate a financial sector in a directed technological change model, where research firms working on different technologies raise funding from financial intermediaries at potentially different costs. We show that, in addition to a rising carbon tax and a generous but short-lived clean research subsidy, optimal climate policies include a clean finance subsidy directly aimed at reducing the financing cost differential across technologies. The presence of an endogenous financing experience effect induces stronger mitigation efforts in the short-term to accelerate the convergence of heterogeneous financing costs. This is achieved primarily through a carbon price premium of 39% in 2025, relative to a case with no financing costs.