Transition-metal dichalcogenides (TMDCs) are an aspiring class of materials with unique electronic and optical properties and potential applications in spin-based electronics. Here, terahertz emission spectroscopy is used to study spin-to-charge current conversion (S2C) in the TMDC NbSe2 in ultra-high-vacuum-grown F|NbSe2 thin-film stacks, where F is a layer of ferromagnetic Fe or Ni. Ultrafast laser excitation triggers an ultrafast spin current that is converted into an in-plane charge current and, thus, a measurable THz electromagnetic pulse. The THz signal amplitude as a function of the NbSe2 thickness shows that the measured signals are fully consistent with an ultrafast optically driven injection of an in-plane-polarized spin current into NbSe2. Modeling of the spin-current dynamics reveals that a sizable fraction of the total S2C originates from the bulk of NbSe2 with the opposite, negative sign of the spin Hall angle as compared to Pt. By a quantitative comparison of the emitted THz radiation from F|NbSe2 to F|Pt reference samples and the results of ab initio calculations, it is estimated that the spin Hall angle of NbSe2 for an in-plane polarized spin current lies between -0.2% and -1.1%, while the THz spin-current relaxation length is of the order of a few nanometers