Within the context of heavy neutral lepton (HNL) extensions of the Standard Model, we compute the cross-sections for \( {\mu}^{+}{e}^{-}\to {\ell}_{\alpha}^{+}{\ell}_{\beta}^{-} \) scattering, as well as several angular observables. In particular, we investigate the future sensitivity of a μTRISTAN collider in discovering such charged lepton flavour violating processes and the potential constraining power of these searches on the parameter space of HNL models. Our results show that while low-energy probes of μ − e flavour violation do offer the most promising potential, the prospects for eτ and μτ flavour violation searches at μTRISTAN can exceed those of related low-energy probes (as well as flavour violating Z-pole processes at FCC-ee) by several orders of magnitude.
