An integrated two-stage metallurgical process has been developed to process concentrates from the Olimpiadinskoe deposit, which contain high levels of antimony and arsenic. The optimal parameters for the alkaline sulfide leaching process of the initial concentrate from the Olimpiadinskoe deposit were determined to achieve the maximum extraction of antimony at a 99% level. The recommended parameters include an L:S ratio of 4.5:1, a sodium sulfide concentration of 61 g/L, a sodium hydroxide concentration of 16.5 g/L, a duration of 3 h, and a temperature of 50 °C. A synergistic effect of co-processing alkaline sulfide leach cakes with sulfuric and nitric acids was observed. The pre-treatment step reduced the nitric acid composition by converting carbonates into gypsum and increased the arsenic extraction by 15% during subsequent nitric acid leaching. The laboratory research on the nitric acid leaching of decarbonized cake established the key parameters for the maximum iron and arsenic extraction in solution (92% and 98%, respectively), including an L:S ratio of 9:1, a nitric acid concentration of 6 mol/L, and a time of 90 min. Full polynomial equations for the iron and arsenic extraction from the decarbonized cake were derived. The model demonstrated a high relevance, as evidenced by the determination coefficients (R2) of 96.7% for iron and 93.2% for arsenic. The technology also achieved a high gold recovery rate of 95% from the two-stage alkaline sulfide and nitric acid leach cake. Furthermore, the maximum deposition of arsenic from the nitrate leach solution in the form of insoluble As2S3was determined to be 99.9%. A basic technological flow sheet diagram for processing the flotation gold–antimony concentrate from the Olimpiadinskoe deposit was developed, including two stages: the production of metallic antimony and the gold extraction from the nitric leach cake.