We combine first-principles density-functional theory, Berry-curvature analysis, semiclassical Boltzmann transport, and atomistic spin dynamics to establish hexagonal NiS as a compensated $3d$ altermagnetic semimetal in which topology, magnetism, and lattice dynamics are intrinsically intertwined. The rotational coset symmetry of the NiAs lattice produces the momentum-dependent spin splitting characteristic of altermagnetism. With spin-orbit coupling, gapped Dirac-like crossings generate intense Berry-curvature hot spots and nearly compensated electron-hole pockets. This leads to a large and anisotropic intrinsic spin Hall conductivity comparable to that of several $4d/5d$ metals, a symmetry-allowed anomalous Hall response despite zero net magnetization, and nonsaturating magnetoresistance exceeding ${10}^3\%$. On the magnetic side, first-principles determination of the exchange tensor reveals dominant long-range superexchange and sizable anisotropic interactions, quantitatively reproducing the experimental Néel temperature. Our results identify NiS as a model $3d$ platform in which carrier compensation, altermagnetic symmetry, Berry-curvature–driven transport, and lattice-sensitive magnetism coexist within a single symmetry framework, offering a design principle for multifunctional quantum responses in correlated transition-metal compounds.

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• Density of states
• Electronic structure
• Fermi surface
• Magnetic coupling
• Magnetic interactions
• Magnetotransport
• Spin dynamics
• Spin-orbit coupling
• Spin-phonon coupling
• Boltzmann theory
• Density functional theory
• First-principles calculations