COVID-19 pandemic and its recovery bring opportunities and threats for global climate governance and further challenge climate related assets. In this study, we analyze the efficiency of government response policies and fiscal policies on green recovery by observing the variation characteristics of carbon allowance prices in the EU emission trading system (EU ETS). Using the OLS and threshold methods in the original time scales, we find that: (1) The EUA prices had an inverted U-shaped relationship with the number of new confirmed cases and deaths. (2) Government response policies had a better effect than fiscal policies when mitigating the negative impact of the pandemic. After decomposing and reconstructing the time series, the multiscale analysis indicates that: (3) The carbon price fluctuated in the short term with the increasing number of newly confirmed cases (or deaths) but gradually recovered due to the recovery policies. (4) Government response policies had a "stop-loss" effect in the short term, and then working alongside fiscal policies, sustained and promoted the development of the EU ETS and green recovery. In the post-COVID-19 era, we suggest the combination of various policies to convert the current health crisis into opportunities for climate change mitigation.