We examine how climate-related (transition and physical) risks impact European bond markets and inflation expectations, and identify their effects across distinct volatility regimes using a Markov-switching vector autoregression model. Our central finding is that the transmission of climate-related risk shocks is highly state-dependent and primarily affects short-term inflation expectations. Transition risks have a limited, disinflationary effect on short-term expectations, but only during low volatility periods. In sharp contrast, physical risks exert a destabilising, inflationary impact during high volatility periods, depressing bond returns and amplifying market stress. Additionally, we observe two more patterns: first, that long-term inflation expectations tend to remain largely anchored. Second, financial linkages and contagion tend to intensify in the high volatility state. Our findings matter for asset pricing and for monetary authorities. They support integrating climate-related risks into stability frameworks, as these shocks presumably intensify and complicate the trade-off between inflation-target credibility and financial stability.