Climate change and the associated rise in global temperature have accelerated the melting glaciers and also forced changes in precipitation patterns across glaciated terrains. Several factors influence the response of glaciers to climate change, including the local climate setting and bed characteristics. Additionally, meltwater influx into the glacier-bed interface during the ablation season can alter the subglacial drainage conditions and potentially influence the glacier flow rate. Direct observations of the subglacial environment are challenging due to the inaccessibility of this environment. However, numerical models of ice flow and subglacial hydrology in association with surface observations can be used to better understand processes at the glacier bed interface that impact glacier evolution. Here, we use GlaDS (Glacier Drainage System Model) on a mountain glacier to simulate the evolution of the subglacial drainage system beneath the Drang Drung Glacier in the Zanskar Basin, Ladakh Himalayas to understand the physical processes impacting the glacier flow rate. We also use repeat satellite observations over the period 2020-2021 to quantify variability in the glacier velocity at monthly scales and to infer the linkages between the subglacial hydrology and the surface. The results from this modelling framework provide insights into the temporal evolution of the subglacial hydrological system and its role in controlling the observed variations in glacier velocity. Our modelling exercises will deepen our understanding of the linkages between subglacial hydrology, ice dynamics, and glacier response in a region where communities are reliant on glaciers for water. More generally, our work will provide insights into controls on the future evolution of mountain glaciers under climate change.