  A number of measurements in decays induced by the semileptonic $b\to s$ and
$b\to c$ transitions hint towards a possible role of new physics in both
sectors. Motivated by these anomalies, we investigate the lepton flavor
violating $B\to K^*_2 (1430)\mu^{\pm}\tau^{\mp}$ decays. We calculate the
two-fold angular distribution of $B\to K^*_2\ell_1\ell_2$ decay in presence of
vector, axial-vector, scalar and pseudo-scalar new physics interactions. We
then compute the branching fraction and lepton forward-backward asymmetry in
the framework of $U^{2/3}_1$ vector leptoquark which is a viable solution to
the current $B$ anomalies. We find that the upper limits are $\mathcal{B}(B\to
K^*_2\mu^-\tau^+)\leq 1.64\times 10^{-7}$ and $\mathcal{B}(B\to
K^*_2\mu^+\tau^-)\leq 0.60\times 10^{-7}$ at $90\%$ C.L.
