Amorphous metallic alloys, also known as metallic glasses (MGs), are materials with unique physical properties resulting from their disordered yet densely packed atomic structure. The packing density of MGs can be further enhanced by external pressure, forcing the decrease of interatomic distances and modifying both the atomic and electronic structure of an alloy. This work reports on classical molecular dynamics (MD) and density functional theory (DFT) studies of Ni64Zr36 MG in a hydrostatic pressure range of 0–120 GPa. The MD simulations revealed that compression leads to enhanced short-range ordering by increasing the contribution of efficiently packed icosahedral-like clusters. According to the DFT calculations, for pressure above 50 GPa, Zr atoms show a significant change in electronic configuration, with a dominant charge transfer from their s and p to d-states and charge redistribution between Ni and Zr atoms. This variation is correlated with the appearance of pairs with significantly shortened interatomic distances, as detected by the MD. We conclude that the enhanced icosahedral ordering in Ni64Zr36 MG is induced not only by the pressure-driven densification of an alloy but also by a variation of its electronic structure.