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Recently, transition-metal based kagome magnets, consisting of stacked kagome lattices, have shown to provide a natural platform to study the effect of the interplay between magnetism and electronic topology. For example, the ferromagnets Fe₃Sn₂ and Co₃Sn₂S₂ and the antiferromagnets Mn₃Ge and Mn₃Sn have revealed a large observed intrinsic anomalous Hall effect (AHE) and topological band degeneracies. Of particular interest, the ternary kagome magnet TbMn₆Sn₆ has very recently revealed a large intrinsic Chern gapped phase associated with Landau quantization upon application of a magnetic field at low temperature. Here we present our recent findings on the role of the rare-earth metal terbium in the complex interplay of magnetism and topology in the electronic structure of TbMn₆Sn₆. The magnetic structure consists of a collinear ferrimagnet below the Curie temperature of 423K and a spin reorientation process at 310K. The intrinsic AHE is negligible at low temperatures but scales non-monotonically with magnetization at higher temperatures leading to the manifestation of an unconventional intrinsic contribution.