Due to climate change and elevation-dependent warming, the hydrology of mountain regions is rapidly changing, particularly where groundwater interacts with glaciers and permafrost. Widespread alpine glacier retreat and permafrost degradation are well documented, yet their individual and combined effects on groundwater discharge and groundwater-surface water exchange remain poorly constrained. In this study, we develop a two-dimensional coupled groundwater-flow and heat-transport numerical model using the United States Geological Survey SUTRA 4.0 code to evaluate how climate change impacts groundwater discharge dynamics in a permafrost-affected alpine aquifer recharged by glacial meltwater. The model simulates a hillslope-valley cross section adjacent to a small alpine glacier in the Rocky Mountains of Colorado, and is forced with observed baseline and future warming climate scenarios. The simulations explicitly simulate changes to permafrost extent due to subsurface warming, seasonal freeze-thaw cycles, and glacial meltwater recharge to groundwater. The simulation results show that warming promotes the development of supra-permafrost taliks, perennially unfrozen zones within otherwise frozen ground, that reorganize subsurface flow paths and shift both the magnitude and timing of groundwater discharge to a downstream alpine lake. Ongoing numerical experiments quantify system sensitivity to warming rate, permafrost thickness and continuity, and variable glacial meltwater recharge. The research provides process-based insight into groundwater discharge dynamics in degrading permafrost systems and clarifies the role of glacial meltwater recharge in sustaining surface-water flow under continued warming. The results have implications for hydrologic resilience and water resource sustainability in alpine and permafrost-influenced watersheds that are undergoing rapid environmental change.