The measurement of prompt $\mathrm{D}^{*+}$-meson spin alignment in ultrarelativistic heavy-ion collisions with respect to the direction orthogonal to the reaction plane is presented. The spin alignment is quantified by measuring the element $\rho_{00}$ of the diagonal spin-density matrix for prompt $\mathrm{D}^{*+}$ mesons with $3<p_{\mathrm{T}}<30~\mathrm{GeV}/c$ in two rapidity intervals, $|y|<0.3$ and $0.3<|y|<0.8$, in mid-central Pb-Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 5.36 TeV. The measured spin alignment of prompt $\mathrm{D}^{*+}$ mesons is compared with previous measurement at lower collision energies ($\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV) as well as with that of inclusive $J/\psi$ mesons measured at forward rapidity ($2.5<y<4$).