The in-medium properties of $D_S$ mesons are investigated within the framework of an effective hadronic model, which is a generalization of a chiral $SU\left(3\right)$ model, to $SU\left(4\right)$, in order to study the interactions of the charmed hadrons. In the present work, the $D_S$ mesons are observed to experience net attractive interactions in a dense hadronic medium, hence reducing the masses of the $D_S^{+}$ and $D_S^{-}$ mesons from the vacuum values. While this conclusion holds in both nuclear and hyperonic media, the magnitude of the mass drop is observed to intensify with the inclusion of strangeness in the medium. Additionally, in hyperonic medium, the mass degeneracy of the $D_S$ mesons is observed to be broken, due to opposite signs of the Weinberg-Tomozawa interaction term in the Lagrangian density. Along with the magnitude of the mass drops, the mass splitting between $D_S^{+}$ and $D_S^{-}$ mesons is also observed to grow with an increase in baryonic density and strangeness content of the medium. However, all medium effects analyzed are found to be weakly dependent on isospin asymmetry and temperature. We discuss the possible implications emanating from this analysis, which are all expected to make a significant difference to observables in heavy ion collision experiments, especially the upcoming Compressed Baryonic Matter (CBM) experiment at the future Facility for Antiproton and Ion Research (FAIR), GSI, where matter at high baryonic densities is planned to be produced.