We investigate, using a first-principles density functional methodology, the nature of magnetism in monolayer 1T phase of tantalum disulfide (1T-TaS2). Magnetism in the insulating phase of TaS2 is a longstanding puzzle and has led to a variety of theoretical proposals including notably the realization of a two-dimensional quantum-spin-liquid (QSL) phase. By means of noncollinear spin calculations, we derive ab initio spin Hamiltonians including two-spin bilinear Heisenberg exchange as well as biquadratic and four-spin ring-exchange couplings, the latter being relevant for the stabilization of putative QSL states. We find that both quadratic and quartic interactions are consistently ferromagnetic for all the functionals considered. Relativistic calculations predict substantial magnetocrystalline anisotropy. Altogether, our results suggest that this material may realize an easyplane XXZ quantum ferromagnet with large anisotropy.