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We report a comprehensive single-crystal neutron diffraction investigation of the Kitaev quantum magnet $\alpha$-RuCl$_{3}$ under hydrostatic pressure. Utilizing a He-gas pressure cell, we successfully applied an ideal hydrostatic pressure in situ at low temperatures, which allows to effectively eliminate any possible influences from the structural transition occurring between 200 K and 50 K under ambient conditions. Our experiments reveal a gradual suppression of the ziagzag antiferromagnetic order as hydrostatic pressure increases. Furthermore, a reversible pressure-induced structural transition occurs at a critical pressure of $P_d$ = 0.15 GPa at 30 K, as evidenced by the absence of magnetic order and non-uniform changes in lattice constants. The decrease in magnetic transition temperature is discussed in relation to a pressure-induced change in the trigonal distortion of the Ru-Cl octahedra in this compound. Our findings emphasize the significance of the trigonal distortion in Kitaev materials, and provide a new perspective on the role of hydrostatic pressures in the realization of the Kitaev quantum spin liquid state in $\alpha$-RuCl$_{3}$.