  We compute the Standard Model semileptonic vector and axial-vector form
factors for $B_s\to D_s^*$ decay across the full $q^2$ range using lattice QCD.
We use the Highly Improved Staggered Quark (HISQ) action for all valence
quarks, enabling us to normalise weak currents nonperturbatively. We use gluon
field configurations including $u$, $d$, $s$ and $c$ HISQ sea quarks and
multiple HISQ heavy quarks with masses from the $c$ mass up to that of the $b$
on our finest lattices. We determine the physical form factors, with which we
construct the differential and total rates for $\Gamma(B_s^0\to
D_s^{*-}\ell^+{\nu}_\ell)$. We find
$\Gamma_{\ell=e}/|\eta_\mathrm{EW}V_{cb}|^2=2.07(17)_\mathrm{latt}(2)_\mathrm{EM}\times
10^{13} ~\mathrm{s}^{-1}$,
$\Gamma_{\ell=\mu}/|\eta_\mathrm{EW}V_{cb}|^2=2.06(16)_\mathrm{latt}(2)_\mathrm{EM}\times
10^{13} ~\mathrm{s}^{-1}$ and
$\Gamma_{\ell=\tau}/|\eta_\mathrm{EW}V_{cb}|^2=5.14(37)_\mathrm{latt}(5)_\mathrm{EM}\times
10^{12} ~\mathrm{s}^{-1}$, where $\eta_\mathrm{EW}$ contains the electroweak
correction to $G_F$, the first uncertainty is from our lattice calculation, and
the second allows for long-distance QED effects. We compute the ratio
$R(D_s^{*-})\equiv
\Gamma_{\ell=\tau}/\Gamma_{\ell=\mu}=0.2490(60)_\mathrm{latt}(35)_\mathrm{EM}$
and obtain a value for the ratio of decay rates $\Gamma_{\ell=\mu}(B_s\to
D_s)/\Gamma_{\ell=\mu}(B_s\to D_s^*)=0.443(40)_\mathrm{latt}(4)_\mathrm{EM}$,
which agrees well with recent LHCb results. We determine $|V_{cb}|=42.2
(1.5)_\mathrm{latt}(1.7)_\mathrm{exp}(0.4)_\mathrm{EM} \times 10^{-3}$ by
combining our lattice results across the full q^2 range with experimental
results from LHCb. A comparison of our results to the normalised differential
decay rate from LHCb shows good agreement. We also test the impact of new
physics couplings on observables sensitive to lepton flavor universality
violation.
