A wide range of two-dimensional (2D) materials have exhibited anomalous electrical properties when surrendered to pressure, along with the unsolved long-standing mystery of the relationship between dimension and superconductivity (SC). Investigation of group IVB transition-metal trichalcogenides (TMTCs) with anisotropic structures is expected to uncover novel physics and shed more light on this relationship in 2D materials. As a typical member in TMTCs, the $\mathrm{ZrS}{\mathrm{e}}_{3}$ sample with a quasi-one-dimensional structure was discovered to change from a semiconductor into a bulk superconducting phase at 16.0 GPa, evidenced by the electrical transport and alternating-current magnetic susceptibility measurements under pressure. A maximum ${T}_{\mathrm{c}}\ensuremath{-}5.5$ K was achieved at 23.1 GPa, concomitantly with an n-p carrier-type switch considered as Lifshitz transition. Besides, an isostructural phase transition was confirmed via in situ x-ray-diffraction measurement at 25.5 GPa, indicating the preservation of the quasi-one-dimensional structure throughout the pressure range. The present results indicate that the atomic spacing and in-plane anisotropy play an important role in the formation of bulk (filamentary) SC in group IVB TMTCs.