The present research represents an approach toward the recycling of extractive waste inspired by circular economy and sustainability that is developed in accordance with Goal 12 of the United Nations 2030 Agenda for Sustainable Development Goals. A new procedure for the recovery of REEs from fluorite–barite–galena ores with calcite gangue from the Silius mine (Sardinia, Italy) is presented. The considered samples are waste materials of Silius mineralization, collected in the old processing plant of Assemini (near Cagliari). In this orebody, REE minerals consist of prevailing synchysite (a REE-bearing fluorocarbonate) and subordinate xenotime-Y (a Y-bearing phosphate). REE fluorocarbonates are extracted using 50% K2CO3 as the leaching solution, at 100 °C. Using a solution (mL)/sample (g) ratio of 25, about 10% of the total REE content of the considered sample is extracted within 1 h. At the laboratory scale, such alkaline leaching of REE from the waste materials allows the recovery of the CO2 produced as K2CO3 from concentrated KOH, in accordance with a circular flow. Further work is ongoing to scale up the process into a pilot plant, to prove that the method developed within this research can be economically feasible, socially suitable, and environmentally respectful.