What Becomes of Kinematics and Dynamics When Spacetime Goes Missing?

What becomes of the kinematics-dynamics distinction if spacetime is not fundamental, as several approaches to quantum gravity suggest? Two conceptions of this distinction, the temporal evolution and the constraint-based account, coexist within well-confirmed physics. We argue that, where spacetime emergence challenges a fundamental separation between states and principles describing their evolution, the former cannot be straightforwardly maintained. The constraint-based account, by contrast, can, at least in principle, survive without fundamental spacetime. As a case study, we focus on causal set theory to show that such a constraint-based interpretation is available in one non-spatiotemporal approach to quantum gravity, to finally explore the consequences for the possibility of non-spatiotemporal dynamical laws.