We show that the probability of $f\text{\ensuremath{-}}f$ radiative transitions $(^{2}F_{7∕2}\ensuremath{\leftrightarrow}^{2}F_{5∕2})$ of ${\mathrm{Yb}}^{3+}$ ions in gadolinium gallium garnet (GGG) crystals is sensitive to hydrostatic pressure application. The changes of the transition energy with pressure are very small, almost negligible. However, we observed much more pronounced variations of the transition probability, which are ascribed to a coupling between the $4{f}^{13}$ with the $4{f}^{12}5{d}^{1}$ electronic configurations and variations of the coupling coefficient with pressure. The theoretical model, explaining this behavior, assumes nonmonotonic changes of the odd-parity crystal-field terms associated with lattice distortions induced by pressure. The magnitude of these distortions correlates well with the magnitude of the distortion from the noncubic symmetry of the dodecahedral crystallographic sites in GGG host, monitored by the pressure dependence of the splitting of the $^{4}F_{3∕2}$ level of ${\mathrm{Nd}}^{3+}$ ions.