The production yields of non-prompt $D_s^{+}$ mesons, namely $D_s^{+}$ mesons from beauty-hadron decays, were measured for the first time as a function of the transverse momentum ($p_T$) at midrapidity ($\left|y\right|<0.5$) in central and semi-central Pb–Pb collisions at a centre-of-mass energy per nucleon pair $\sqrt{s_{\mathrm{NN}}}=5.02\mathrm{TeV}$ with the ALICE experiment at the LHC. The $D_s^{+}$ mesons and their charge conjugates were reconstructed from the hadronic decay channel $D_s^{+}\to \varphi {\pi }^{+}$, with $\varphi \to K^{-}{K}^{+}$, in the $4<p_T<36\mathrm{GeV}/c$ and $2<p_T<24\mathrm{GeV}/c$ intervals for the 0–10% and 30–50% centrality classes, respectively. The measured yields of non-prompt $D_s^{+}$ mesons are compared to those of prompt $D_s^{+}$ and non-prompt $D^0$ mesons by calculating the ratios of the production yields in Pb–Pb collisions and the nuclear modification factor $R_{\mathrm{AA}}$. The ratio between the $R_{\mathrm{AA}}$ of non-prompt $D_s^{+}$ and prompt $D_s^{+}$ mesons, and that between the $R_{\mathrm{AA}}$ of non-prompt $D_s^{+}$ and non-prompt $D^0$ mesons in central Pb–Pb collisions are found to be on average higher than unity in the $4<p_T<12\mathrm{GeV}/c$ interval with a statistical significance of about $1.6\sigma$ and $1.7\sigma$, respectively. The measured $R_{\mathrm{AA}}$ ratios are compared with the predictions of theoretical models of heavy-quark transport in a hydrodynamically expanding QGP that incorporate hadronisation via quark recombination.