Tree-ring-width chronologies for 33 samples of Picea abies (L.) Karst. were developed, and a relationship between tree growth and hydrometeorological features was established and analyzed. Precipitation, temperature, and discharge records were extrapolated to understand past climate trends to evaluate the accuracy of global climate models (GCMs). Using Machine Learning (ML) approaches, hydrometeorological records were reconstructed/extrapolated back to 1886. An increase in the mean annual temperature (Tmeana) increased the mean annual discharge (Dmeana) via glacier melting; however, no temporal trends in annual precipitation were detected. For these reconstructed climate data, root-mean-square error (RMSE), Taylor diagrams, and Kling–Gupta efficiency (KGE) were used to evaluate and assess the robustness of GCMs. The CORDEX REMO models indicated the best performance for simulating precipitation and temperature over northern Tien Shan; these models replicated historical Tmena and Pa quite well (KGE = 0.24 and KGE = 0.24, respectively). Moreover, the multi-model ensembles with selected GCMs and bias correction can significantly increase the performance of climate models, especially for mountains region where small-scale orographic effects abound.