We study the hadronic matrix elements describing the $B_s \to D_s\ell \bar\nu_\ell$ decay in and beyond the Standard Model. By using the twisted mass QCD on the lattice with $N_f=2$ dynamical flavors we compute the normalization $\mathscr G_s(1)$ of the form factor dominating $B_s\to D_s \ell \bar\nu_\ell$ in the SM. We also make the first lattice determination of $F_0(q^2)/F_+(q^2)$ and $F_T(q^2)/F_+(q^2)$ near zero recoil (near $q^2_{\rm max}$). We briefly discuss the non-strange case $B \to D\ell \bar\nu_\ell$ as well.