Protease-producing yeasts were isolated from potato wastes and screened for protease production on skim milk agar plates. The best producer of protease isolate was identified as Clavispora lusitaniae. The strain showed higher enzyme production using tomato pomace and bread waste mix as a solid fermentation substrate. The optimized conditions improved enzyme activity and showed a maximal production of 33,450 ± 503 IU/g compared with the initial activity of 11,205.78 ± 360 without medium optimization. A threefold increase in protease activity after medium optimization proved the reliability of using the PBD and CCD design. A 19.76-fold purified enzyme and a yield of 32.94% were obtained after purification. The protease showed maximum activity at pH 4 and 60 °C and was resistant to Tween 20, Tween 80, SDS, and β-mercaptoethanol, Ca2+, and Mg2+ stimulated it. The protease activity was strongly inhibited in the presence of urea, and EDTA. The results revealed Clavispora lusitaniae protease’s ability to degrade wheat seeds and flour gluten by 98.7% and 97% respectively under pH 4 for 24 h at 40 °C. According to this study, this enzyme could be a potential candidate for the food industry, particularly for treating wheat seed and flour to reduce the immunogenicity of gluten.