  We study the exclusive semileptonic decays B_s->D_{s0}^*\ell\bar\nu and
B_s->D_{s1}^*\ell\bar\nu, where p-wave excited D_{s0}^* and D_{s1}^* states are
identified with the newly observed D_{sJ}(2317) and D_{sJ}(2460) states. Within
the framework of HQET the Isgur-Wise functions up to the subleading order of
the heavy quark expansion are calculated by QCD sum rules. The decay rates and
branching ratios are computed with the inclusion of the order of 1/m_Q
corrections. We point out that the investigation of the B_s semileptonic decays
to excited D_s mesons may provide some information about the nature of the new
D_{sJ}^* mesons.
