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Under the assignment of $D_s(3040)$ as a radially excited p-wave $\bar cs$state with $J^P=1^+$, we compute the $B_s\to D_s (3040)$ form factors withinthe covariant light-front quark model. Two classification schemes for thep-wave $\bar cs$ meson are adopted. We also use our results to predict thebranching ratios (BRs), polarization fractions and angular asymmetries insemileptonic $B_s\to D_s(3040)\ell\bar\nu(\ell=e,\mu,\tau)$. The BRs are foundto have the order of $10^{-3}$ for $\ell=e,\mu$ and $10^{-5}$ for $\ell=\tau$.We find that the polarization fractions and the angular asymmetries could beuseful to pin down the ambiguities of the quantum numbers for $D_s(3040)$. Inaddition, we investigate the nonleptonic $B_s\to D_s(3040)M$ decays under thefactorization method, where $M$ denotes a charged pseudoscalar or a vectormeson. The BRs of $B_s\to D_s(3040)\rho$ and $B_s\to D_s(3040)D_s^*$ reach theorder of $10^{-3}$, while the other channels are typically smaller by 1-2orders.

$B_s\to D_s(3040)$ form factors and $B_s$ decays into $D_s(3040)$