  We study the semileptonic decay $\bar{B}_s \to K^{*+} \ell^-\bar\nu_\ell$,
which is induced by $b\to u \ell^- \bar\nu_\ell$ transitions at the quark
level. We take into account the standard model (SM) operator from $W$-boson
exchange as well as possible extensions from physics beyond the SM. The
secondary decay $K^{*+}\to K\pi$ can be used to study a number of angular
observables, which are worked out in terms of short-distance Wilson
coefficients and hadronic form factors. Our analysis allows for an independent
extraction of the Cabibbo-Kobayashi-Maskawa matrix element $|V_{ub}|$ and for
the determination of certain ratios of $\bar{B}_s\to K^*$ form factors.
Moreover, a future precision measurement of the forward-backward asymmetry in
the $\bar{B}_s \to K^{*+} \ell^-\bar\nu_\ell$ decay can be used to
unambiguously verify the left-handed nature of the transition operator as
predicted by the SM. We provide numerical estimates for the relevant angular
observables and the resulting decay distributions on the basis of available
form-factor information from lattice and sum-rule estimates. In addition, we
pay particular attention to suitable combinations of angular observables in the
decays $\bar{B}_s \to K^{*+}(\to K\pi)\ell^-\bar\nu_\ell$ and $\bar{B} \to
K^{*0}(\to K\pi)\ell^+\ell^-$, and find that they provide complementary
constraints on the relevant $b\to s$ short-distance coefficients. As a
by-product, we perform a SM fit on the basis of selected experimental decay
rates and hadronic input functions, which results in $|V_{ub}| = (4.07 \pm
0.20) \cdot 10^{-3}$.
