  The nuclear modification factor ${R}_{\rm AA}$ and the elliptic flow
coefficient ${v}_{\rm 2}$ of charm-strange meson $D^{+}_{s}$ is systematically
studied in Pb--Pb collisions at $\sqrt{s_{\rm NN}}=5.02~{\rm TeV}$ and
$2.76~{\rm TeV}$. During the modeling, the coupling strength between the
injected charm quark and the incident medium constituents, is extracted from
the lattice QCD calculations: $2\pi TD_{s}=7$ (\textbf{Model-A}) and $2\pi
TD_{s}=1.3 + (T/T_{c})^2$ (\textbf{Model-B}). We find that, comparing ${R}_{\rm
AA}(D^{+}_{s})$ with ${R}_{\rm AA}(non-strange)$, the heavy-light coalescence
effect is more pronounced for the former one, resulting in an enhancement
behavior in the range $2\lesssim {p}_{\rm T}\lesssim5~{\rm GeV}$. The
predictions of ${R}_{\rm AA}(D^{+}_{s})$ and ${R}_{\rm AA}(non-strange)$ favor
Model-A to have a better description of the measured ${p}_{\rm T}$ dependence
in both energies, while their ${v}_{\rm 2}$ prefer Model-B at moderate
${p}_{\rm T}$ ($2\lesssim {p}_{\rm T}\lesssim4~{\rm GeV}$). Therefore, it is
necessary to consider the temperature- and/or momentum-dependence of $2\pi
TD_{s}$ to describe simultaneously ${R}_{\rm AA}(D^{+}_{s})$ and ${v}_{\rm
2}(D^{+}_{s})$ in different centrality classes in Pb--Pb collisions.
