Although the Greenland Ice Sheet (GrIS) is losing mass at an accelerating rate, much uncertainty remains about how surface runoff interacts with the subglacial drainage system and affects water pressures and ice velocities, both currently, and into the future. Here, we apply a physically-based, subglacial hydrological model to the Paakitsoq region, west Greenland, and run it into the future to calculate patterns of daily subglacial water pressure fluctuations in response to climatic warming. The model is driven with moulin input hydrographs calculated by a surface routing model, forced with distributed runoff. Surface runoff and routing are simulated for a baseline year (2000), before the model is forced with future climate scenarios for the years 2025, 2050 and 2095, based on the IPCC’s Representative Concentration Pathways (RCPs). Our results show that as runoff increases throughout the 21st century, and/or as RCP scenarios become more extreme, the subglacial drainage system makes an earlier transition from a less efficient network operating at high water pressures, to a more efficient network with lower pressures. This will likely cause an overall decrease in ice velocities for marginal areas of the GrIS. However, short-term variations in runoff, and therefore subglacial pressure, can still cause localized speedups, even after the system has become more efficient. If these short-term pressure fluctuations become more pronounced as future runoff increases, the associated late-season speedups may help to compensate for the drop in overall summer velocities, associated with earlier transitioning from a high to a low pressure system.