In this forum, we highlight a discord in strategies around climate change policy and politics. On one hand, there is widespread concern for the pursuit of climate policy stability: stability in the design of policy and institutions, but particularly making policy and institutional development irreversible. However, much recent literature has revived an insistence on the inevitability of political conflict for pursuing the often large transitions needed to mitigate and adapt to accelerating climate change. Here, addressing climate change requires conflict, to weaken the power of incumbent actors that have blocked ambitious climate policy enactment for decades. Scholarship deploying each perspective tends to explicitly accept the need for radical sociotechnical transformations to address the climate crisis, but each entails radically different approaches to how to pursue decarbonization. The article outlines a research agenda focused on thinking about how these two apparently contradictory dynamics in climate politics interact, to advance our understanding of what sorts of strategies might open up political space for rapid transformations.