  We present a new calculation of the semileptonic tree-level and
flavor-changing neutral current form factors describing $B$-meson transitions
to tensor mesons $T=D_2^*,K_2^*,a_2,f_2$ ($J^{P}=2^{+}$). We employ the QCD
Light-Cone Sum Rules approach with $B$-meson distribution amplitudes. We go
beyond the leading-twist accuracy and provide analytically, for the first time,
higher-twist corrections for the two-particle contributions up to twist four
terms. We observe that the impact of higher twist terms to the sum rules is
noticeable. We study the phenomenological implications of our results on the
radiative ${B} \to K_2^{*}\gamma$ and semileptonic ${B} \to D_2^* \ell {\bar
\nu}_\ell$, ${B} \to K_2^{*}\ell^+\ell^-$ decays.
