The excitation efficiency and external luminescence quantum efficiency of trivalent Eu3+ ions doped into gallium nitride (GaN) was studied under optical and electrical excitation. For small pump fluences it was found that the excitation of Eu3+ ions is limited by an efficient carrier trap that competes in the energy transfer from the host material. For large pump fluences the limited number of high-efficiency Eu3+ sites, and the small excitation cross-section of the majority Eu3+ site, limit the quantum efficiency. At low temperatures under optimal excitation conditions, the external luminescence quantum efficiency reached a value of 46%. These results show the high potential for this material as an efficient light emitter, and demonstrates the importance of the excitation conditions on the light output efficiency.