Na$_{2}$OsO$_{4}$ is an unusual quantum material that, in contrast to the common 5${d}^{2}$ oxides with spins = 1, owns a magnetically silent ground state with spin = 0 and a band gap at Fermi level attributed to a distortion in the OsO$_{6}$ octahedral sites. In this semiconductor, our low-temperature electrical transport measurements indicate an anomaly at 6.3 K with a power-law behavior inclining through the semiconductor-to-metal transition observed at 23 GPa. Even more peculiarly, we discover that before this transition, the material becomes more insulating instead of merely turning into a metal according to the conventional wisdom. To investigate the underlying mechanisms, we applied experimental and theoretical methods to examine the electronic and crystal structures comprehensively, and conclude that the enhanced insulating state at high pressure originates from the enlarged distortion of the OsO$_{6}$. It is such a distortion that widens the band gap and decreases the electron occupancy in Oss ${t}_{2g}$ orbital through an interplay of the lattice, charge, and orbital in the material, which is responsible for the changes observed in our experiments.
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