We report neutron scattering experiments which reveal a large spin gap in the magnetic excitation spectrum of weakly-monoclinic double perovskite Sr2ScOsO6. The spin gap is demonstrative of appreciable spin-orbit-induced anisotropy, despite nominally orbitally-quenched 5d3 Os5+ ions. The system is successfully modeled including nearest neighbor interactions in a Heisenberg Hamiltonian with exchange anisotropy. We find that the presence of the spin-orbit-induced anisotropy is essential for the realization of the type I antiferromagnetic ground state. This demonstrates that physics beyond the LS or JJ coupling limits plays an active role in determining the collective properties of 4d3 and 5d3 systems, and that theoretical treatments must include spin-orbit coupling.