We report the observation of an antipolar phase in cubic ${\mathrm{GaNb}}_{4}{\mathrm{S}}_{8}$ driven by an unconventional microscopic mechanism, the cooperative Jahn-Teller effect of ${\mathrm{Nb}}_{4}{\mathrm{S}}_{4}$ molecular clusters. The assignment of the antipolar nature is based on sudden changes in the crystal structure and a strong drop of the dielectric constant at ${T}_{\mathrm{JT}}=31\text{ }\text{ }\mathrm{K}$, also indicating the first-order nature of the transition. In addition, we found that local symmetry lowering precedes long-range orbital ordering, implying the presence of a dynamic Jahn-Teller effect in the cubic phase above ${T}_{\mathrm{JT}}$. Based on the variety of structural polymorphs reported in lacunar spinels, also including ferroelectric phases, we argue that ${\mathrm{GaNb}}_{4}{\mathrm{S}}_{8}$ may be transformable to a ferroelectric state, which would further classify the observed antipolar phase as antiferroelectric.