​We identify a dominant light-emitting center in ion-implanted GaN:Eu3+ for which the lattice damage has been completely healed, according to x-ray diffraction and Rutherford backscattering spectrometry measurements, by high-temperature, high-pressure annealing. This center is likely to be the isolated substitutional EuGa defect. It lacks a 'subgap' excitation band and therefore has no state in the GaN band gap, shows threefold splitting of its 7F2 level, with two sublevels nearly degenerate, and exhibits a long, single-exponential luminescence decay. Competing luminescent centers of GaN:Eu involve this prime center with intrinsic lattice defects, one of which may also be responsible for the GaN yellow band.