$\ensuremath{\alpha}$-Quartz-type gallium phosphate and representative compositions in the $\mathrm{AlP}{\mathrm{O}}_{4}\text{\ensuremath{-}}\mathrm{GaP}{\mathrm{O}}_{4}$ solid solution were studied by x-ray powder diffraction and absorption spectroscopy, Raman scattering, and by first-principles calculations up to pressures of close to 30 GPa. A phase transition to a metastable orthorhombic high-pressure phase along with some of the stable orthorhombic $Cmcm\mathrm{CrV}{\mathrm{O}}_{4}$-type material is found to occur beginning at 9 GPa at $320{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{\circ}}\mathrm{C}$ in $\mathrm{GaP}{\mathrm{O}}_{4}$. In the case of the $\mathrm{AlP}{\mathrm{O}}_{4}\text{\ensuremath{-}}\mathrm{GaP}{\mathrm{O}}_{4}$ solid solution at room temperature, only the metastable orthorhombic phase was obtained above 10 GPa. The possible crystal structures of the high-pressure forms of $\mathrm{GaP}{\mathrm{O}}_{4}$ were predicted from first-principles calculations and the evolutionary algorithm USPEX. A predicted orthorhombic structure with a $Pmn{2}_{1}$ space group with the gallium in sixfold and phosphorus in fourfold coordination was found to be in the best agreement with the combined experimental data from x-ray diffraction and absorption and Raman spectroscopy. This method is found to very powerful to better understand competition between different phase transition pathways at high pressure.