Much existing research on climate, conflict, and security asks a relatively narrow question: how does climate change trigger or exacerbate violent conflict in ways that threaten stability within the current international system? Far less attention has been paid to how the properties of that system contribute to climate-related risks of violence, conflict, and instability. In this article, we identify three aspects of the structure and workings of what we refer to as the ”international security order” that, in our view, must be brought much more centrally into future research: the multi-dimensional role of war and war preparation as drivers of the climate problem; the widespread use of violence to suppress climate activism; and the failure of climate-policy mechanisms to account for the conflict risk they may create or exacerbate (an effect sometimes referred to as “backdraft”). We argue that these three are not simply contextual factors for climate-related violence. Rather, they work through the climate variable to shape conflict risk. Models and conceptual frameworks that do not explore these and other such connections may be missing important causes and mechanisms of climate-linked insecurity.