First-principles calculations are presented for the ${V}_{\mathrm{Zn}}$ and ${V}_{\mathrm{Ge}}$ cation vacancies and the ${\mathrm{Zn}}_{\mathrm{Ge}}$ and ${\mathrm{Ge}}_{\mathrm{Zn}}$ antisites in ${\mathrm{ZnGeP}}_{2}$, using full-potential linearized muffin-tin orbital method supercell calculations in the local-density approximation to density-functional theory. Under Zn-poor conditions, the lowest Gibbs energy defects are found to be the ${\mathrm{Ge}}_{\mathrm{Zn}}$ and ${V}_{\mathrm{Zn}}$ defects, leading to a compensated $p$-type material in agreement with experimental evidence. The occupation energy levels of the defects are determined and compared with available experimental information. As expected, the ${\mathrm{Ge}}_{\mathrm{Zn}}$ is found to be a donor while the other three are acceptors. Good agreement is obtained with optical quenching and activation of electron paramagnetic resonance signal studies if a direct transfer of electrons from ${\mathrm{V}}_{\mathrm{Zn}}^{2\ensuremath{-}}$ to ${\mathrm{Ge}}_{\mathrm{Zn}}^{2+}$ is assumed rather than a process via the conduction band. This suggests a close association of the dominant acceptors and donors. This is further confirmed by showing that the formation of complexes consisting of two ${V}_{\mathrm{Zn}}^{\ensuremath{-}}$ with a single ${\mathrm{Ge}}_{\mathrm{Zn}}^{2+}$ antisite are favorable in energy. The ${V}_{\mathrm{Ge}}$ on the other hand is found to have high energy of formation under any chemical potential conditions and is found to be unstable toward formation of a ${V}_{\mathrm{Zn}}$ and ${\mathrm{Zn}}_{\mathrm{Ge}}$ pair. Structural relaxation of all defects is performed but no symmetry breaking distortions are found. As a result, the defect wave functions of the unpaired electron in the ${V}_{\mathrm{Zn}}^{\ensuremath{-}}$ is found to be spread equally over the four neighboring P atoms, in disagreement with electron nuclear double resonance data which indicate primary localization on a pair of P atoms. Several possible origins for this discrepancy are discussed.