  In this paper, we show an explicit way to realize a TeV-scale vector
leptoquark from the Pati-Salam (PS) unification with extra vectorlike families.
The leptoquark mass is constrained to be heavier than PeV-scale by the
measurement of a flavor violating kaon decay, $K_L \to \mu e$, in conventional
models. This strong constraint can be avoided by introducing vectorlike
families consistently with the quark and lepton masses and CKM and PMNS
matrices. The other flavor violating processes are also suppressed. In this
model, the vector leptoquark can be sufficiently light to explain the recent
$b\to s\mu\mu$ anomaly, while the $b\to c\tau\nu$ anomaly is difficult to be
explained due to the strong constraints from the $Z^\prime$ boson and
vectorlike quark searches at the LHC. When the $b\to s\mu\mu$ anomaly is
explained, we show that $\mathcal{O}({0.2})$ % tuning is required in the
fermion matrix, the future experiments in $\mu\to e\gamma$ and $\mu$-$e$
conversions will cover the most available parameter space, and sizable neutral
meson mixings, induced by the extra Higgs doublets, are unavoidable.
