  The vector leptoquark representation, $U_\mu = (3,1,2/3)$, was recently
identified as an exceptional single mediator model to address experimental
hints on lepton flavour universality violation in semileptonic $B$-meson
decays, both in neutral ($b \to s \mu \mu$) and charged ($b \to c \tau \nu$)
current processes. Nonetheless, it is well-known that massive vectors crave an
ultraviolet (UV) completion. We present the first full-fledged UV complete and
calculable gauge model which incorporates this scenario while remaining in
agreement with all other indirect flavour and electroweak precision
measurements, as well as, direct searches at high-$p_T$. The model is based on
a new non-abelian gauge group spontaneously broken at the TeV scale, and a
specific flavour structure suppressing flavour violation in $\Delta F = 2$
processes while inducing sizeable semileptonic transitions.
