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We consider a new massive vector boson ${Z}^{\ensuremath{'}}$ that couples to leptons through the ${L}_{\ensuremath{\mu}}$-${L}_{\ensuremath{\tau}}$ current and to quarks through an arbitrary set of couplings. We show that such a model can be obtained from a renormalizable field theory involving new heavy fermions in an anomaly-free representation. The model is a candidate explanation for the discrepancy observed recently by the LHCb Collaboration in angular distributions of the final state particles in the rare decay $B\ensuremath{\rightarrow}{K}^{*}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$. Interestingly, the new vector-boson contribution to the decay $\ensuremath{\tau}\ensuremath{\rightarrow}\ensuremath{\mu}{\ensuremath{\nu}}_{\ensuremath{\tau}}{\overline{\ensuremath{\nu}}}_{\ensuremath{\mu}}$ can also remove a small tension in the measurement of the corresponding branching ratio. Constraints from light flavor meson-mixing restrict the coupling to the up- and down-quarks to be very small and thus direct production of the vector boson at hadron colliders is strongly suppressed. The most promising ways to test the model is through the measurement of the Z decay to four leptons and through its effect on neutrino trident production of muon pairs. This latter process is a powerful but little-known constraint, which surprisingly rules out explanations of $(g\ensuremath{-}2{)}_{\ensuremath{\mu}}$ based on ${Z}^{\ensuremath{'}}$ gauge bosons coupled to muon number, with mass of at least a few GeV.