Pakistan is water stressed, and its water resources are vulnerable due to uncertain climatic changes. Uncertainties are inherent when it comes to the modeling of water resources. The predicted flow variation in the Kunhar River Basin was modeled using the statistically decreased high-resolution general circulation model (GCM) as an input for the Hydrologiska Byråns Vattenbalansavdelning (HBV) model to assess the hydrological response of the Kunhar River Basin under prevailing climate changes. The model’s best performance during the calibration and validation stages was obtained with a regular 0.87 and 0.79 Nash–Sutcliffe efficiency in the basin, respectively. Under the high-end emission scenario, a 122% increase was expected in evapotranspiration in the rising season of months during the winter period 2059–2079, and such developments were attributed to an immense increase in liquid precipitation and temperature. The model’s output reflects a potential for basin stream flow in terms of increasing liquid precipitation up to 182% at the beginning of the monsoon season in the period 2059–2079 in the scenario of high-end emissions. Moreover, the study produced possible uncertainties in high-elevation zones, where the modeling of a catchment can lead to typical snow ablation and accumulation in future projections. This study revealed that the precipitation rate will increase annually, resulting in an increase in the summer stream flow over the basin, though snow is hardly expected to accumulate in the basin’s future climate.