The energy sector provides fuel for much of everyday life, particularly economically and socially. Fighting against the COVID-19 pandemic, a well-functioning and resilient energy sector is vital for maintaining the operation of critical infrastructures, including, most importantly, the health sector, and timely economic recovery. Notwithstanding its importance in everyday life and crises, the energy sector itself is currently in a complex and far-reaching transformation to combat climate change whilst supporting the transition to a low-carbon economy and society, mainly through the development of variable renewable energy sources (RES) such as wind and solar photovoltaics. This paper highlights the need for energy resilience as countries face the triple challenge of the COVID-19 health crisis, the consequent economic crisis, and the climate crisis. Focusing on Europe, it is advanced here that with the ability to balance fluctuating electricity generation and demand, flexibility allows the energy sector to utilise low-carbon RES reliably, ensuring a more resilient and sustainable energy future. This paper derives five urgent policy recommendations for Europe that address possible impacts of COVID-19 on the economic and societal prerequisites for flexibility in energy systems.