The effect of pressure on the electronic and magnetic properties of the antiferromagnetic (TN~43 K) narrow gap semiconductor UNiSn has been investigated by 119Sn Mössbauer spectroscopy and nuclear forward scattering of synchrotron radiation, electrical resistance, and x-ray diffraction. We show that the decrease of the semiconducting gap which leads to a metallic state at p~9 GPa is associated with an enhancement of TN. At higher pressures, both TN and the transferred magnetic hyperfine field decrease, with a collapse of magnetism at ~18.5 GPa. The results are explained by a volume-dependent competition between indirect Ruderman-Kittel-Kasuya-Yosida interaction and the 5f-ligand hybridization.