The deficient management of plastic waste has caused a serious worldwide environmental problem. Thus, one of the main challenges for the industry in the plastics sector in contributing to sustainability and a circular economy consists of providing a subsequent service life to this waste. For that purpose, the appropriate incorporation of antioxidants will play a key role in preventing or postponing the degradation of plastic waste, where the formation of radicals is initiated during its previous lifetime by the action of degrading agents. Functionalized particles, based on mesoporous MCM-41 silica with Irganox 1076, were prepared with two different protocols and were further incorporated into a material containing virgin PP and 30 wt.% of recycled PP, with the purpose of guaranteeing thermal stability during its next service life. A very significant increase in the thermal stability of the resulting composites was found, attributable to the synergistic action between the Irganox 1076 antioxidant and the MCM-41 particles. In addition, the presence of hybrid particles leads to an important nucleating effect for the crystallization of PP. Moreover, a reinforcing role was also played by these modified mesoporous silicas in the resultant systems. The presented methodology constitutes, therefore, a promising strategy for contributing to the circular economy—since the synergy between the Irganox 1076 antioxidant and MCM-41 particles was found to play an important role in the ultimate performance of recycled polyolefins.