Many centralized assignment systems seek to not only provide good matches for participants’ current needs, but also to accommodate changes in preferences and circumstances. We study the problem of designing a dynamic reassignment mechanism in the context of Norway’s system for allocating patients to general practitioners (GPs). We provide direct evidence of misallocation under the current system-patients sitting on waitlists for each others’ GPs, but who cannot trade-and analyze an alternative mechanism that adapts the Top-Trading Cycles (TTC) algorithm to a dynamic environment. In contrast to the static case, dynamic TTC may leave some agents worse off relative to a status quo where trades are not permitted, introducing novel concerns about fairness. We empirically evaluate how this mechanism would perform by estimating a structural model of switching behavior and GP choice. While introducing TTC would on average reduce waiting times and increase patient welfare-with especially large benefits for female patients and recent movers-patients endowed with undesirable GPs would be harmed. Adjustments to the priority system can avoid harming this group while preserving most of the gains from TTC.