  Leptoquarks are ubiquitous in several extensions of the Standard Model and
seem to be able to accommodate the universality-violation-driven
$B$-meson-decay anomalies and the $(g-2)_\mu$ discrepancy interpreted as
deviations from the Standard Model predictions. In addition, the search for
lepton-flavour violation in the charged sector is, at present, a major research
program that could also be facilitated by the dynamics generated by
leptoquarks. In this article, we consider a rather wide framework of both
scalar and vector leptoquarks as the generators of lepton-flavour violation in
processes involving the tau lepton. We single out its couplings to leptoquarks,
thus breaking universality in the lepton sector, and we integrate out
leptoquarks at tree level, generating the corresponding dimension-6 operators
of the Standard Model Effective Field Theory. In Ref. [1] we obtained
model-independent bounds on the Wilson coefficients of those operators
contributing to lepton-flavour-violating hadron tau decays and $\ell$-$\tau$
conversion in nuclei, with $\ell=e,\mu$. Hence, we use those results to
translate the bounds into the couplings of leptoquarks to the Standard Model
fermions.
