We have investigated the electronic structure of the dilute magnetic semiconductor (DMS) $Ga_{0.98}Mn_{0.02}P$ and compared it to that of an undoped $GaP$ reference sample, using hard X-ray photoelectron spectroscopy (HXPS) and hard X-ray angle-resolved photoemission spectroscopy (HARPES) at energies of about 3 keV. We present experimental data, as well as theoretical calculations, in order to understand the role of the Mn dopant in the emergence of ferromagnetism in this material. Both core-level spectra and angle-resolved or angle-integrated valence spectra are discussed. In particular, the HARPES experimental data are compared to free-electron final-state model calculations and to more accurate one-step photoemission theory. The experimental results show differences between $Ga_{0.98}Mn_{0.02}P$ and $GaP$ in both angle-resolved and angle-integrated valence spectra. The $Ga_{0.98}Mn_{0.02}P$ bands are broadened due to the presence of Mn impurities that disturb the long-range translational order of the host $GaP$ crystal. Mn-induced changes of the electronic structure are observed over the entire valence band range, including the presence of a distinct impurity band close to the valence-band maximum of the DMS. These experimental results are in good agreement with the one-step photoemission calculations, and a prior HARPES study of $Ga_{0.97}Mn_{0.03}As$ and $GaAs$ (Gray et al. Nature Materials 11, 957 (2012)), demonstrating the strong similarity between these two materials. The Mn 2p and 3s core-level spectra also reveal an essentially identical state in doping both $GaAs$ and $GaP$.