The anomalous magnetic moments of leptons represent excellent probes of the Standard Model and therefore also of possible new physics effects.
In particular, the persisting hint of new physics in the muon $g$-2 motivates the investigation of similar effects also in the other leptonic dipoles.
In this work, we examine the new physics sensitivity of the tau $g$-2 at future high-energy Muon Collider.
We show that these facilities can access a number of processes like the Drell-Yan processes
$\mu^+\mu^- \to \tau^+\tau^-(h)$, or vector-boson-fusion processes such
as $\mu^+\mu^- \to \mu^+\mu^-\tau^+\tau^-$ and $\mu^+\mu^-\to \nu_\mu \bar{\nu}_\mu \tau^+\tau^-$ those can probe the tau $g$-2
at the level of $\mathcal{O}(10^{-5}-10^{-4})$, a resolution that is orders
of magnitude better than the current bounds.