An accurate potential energy surface (PES) for the HSiS system based on MRCI+Q calculations extrapolated to the complete basis set limit is presented. Modeled with the double many-body expansion (DMBE) method, the PES provides an accurate description of the long-range interactions, including electrostatic and dispersion terms decaying as R-4, R-5, R-6, R-8, R-10 that are predicted from dipole moments, quadrupole moments, and dipolar polarizabilities, which are also calculated at the MRCI+Q level. The novel PES is then used in quasiclassical trajectory calculations to predict the rate coefficients of the Si + SH → SiS + H reaction, which has been shown to be a major source of the SiS in certain regions of the interstellar medium. An account of the zero-point energy leakage based on various nonactive models is also given. It is shown that the reaction is dominated by long-range forces, with the mechanism Si + SH → SiSH → SSiH → SiS + H being the most important one for all temperatures studied. Although SSiH corresponds to the global minimum of the PES, the contribution from the direct reaction Si + SH → SSiH → SiS + H is less than 0.5% for temperatures higher than 500 K. The rovibrational distributions of the products are calculated using the momentum Gaussian binning method and show that as the temperature is increased the average vibrational quantum number decreases while the rotational distribution spreads up to larger values.