The accelerated demand for data centres has sparked concerns about the energy and climate footprint of Artificial Intelligence (AI). We argue that this challenge can be turned into an opportunity by pairing AI growth with the rapid scaling of energy storage deployment. The AI–energy storage nexus can shorten data centres’ time-to-power and access to 24/7 clean energy, while investments by large digital companies in energy storage innovation and deployment can create spillovers for wider clean and flexible power systems. However, this nexus is not always climate-compatible without appropriate policy and additional clean electricity supply. Here, we discuss how energy storage can reduce peak grid import requirements, improve renewable energy matching, and enhance power quality and reliability for data centres. We also discuss how AI can improve the design, operation, and system integration of energy storage. We conclude with policy recommendations to ensure that the growth of AI compute infrastructure reinforces, rather than slows, clean energy transitions.