  In this work, we study the flavor-changing neutral-current process
$B_{c}\to{D}_{s}^{*}(\to{D}_{s}\pi)\ell^{+}\ell^{-}$ ($\ell$= $e$, $\mu$,
$\tau$). The relevant weak transition form factors are obtained by using the
covariant light-front quark model, in which, the main inputs, i.e., the meson
wave functions of $B_{c}$ and $D_{s}^{*}$, are adopted as the numerical wave
functions from the solution of the Schr\"{o}dinger equation with the modified
Godfrey-Isgur model. With the obtained form factors, we further investigate the
relevant branching fractions and their ratios, and some angular observables,
i.e., the forward-backward asymmetry $A_{FB}$, the polarization fractions
$F_{L(T)}$, and the $CP$-averaged angular coefficients $S_{i}$ and the $CP$
asymmetry coefficients $A_{i}$. We also present our results of the clean
angular observables $P_{1,2,3}$ and $P^{\prime}_{4,5,6,8}$, which can reduce
the uncertainties from the form factors. Our results show that the
corresponding branching fractions of the electron or muon channels can reach up
to $10^{-8}$. With more data being accumulated in the LHCb experiment, our
results are helpful for exploring this process, and deepen our understanding of
the physics around the $b\to{s}\ell^{+}\ell^{-}$ process.
