Over the last decades, circular economy and its implications for sustainability have gained momentum in several socio-economic domains (e.g., academia, industry, politics, society), even though the relationship between them remains poorly understood. This situation has blurred the conceptual definition of both terms, limiting their research and practice effectiveness. To counteract this situation, scholars and policymakers are approaching Circular Economy as able to inspire the development of sustainable development strategies and to increase the sustainability of the current economic system, balancing the need for economic development and the importance of protecting environmental resources and people wellbeing. Drawing on the previous considerations, this study aims to contribute to address this gap, better understanding how a circular economy approach can contribute to challenge the number of sustainability issues that currently affect supply chains. In doing so, the analysis has been focused on the investigation of a specific supply chain, the pasta supply chain. To this end, after a brief theoretical recognition, an interpretative model has been proposed for better recognizing and describing the enhancing actions that—at each supply chain’s stages—can improve process efficiency, output effectiveness and, therefore, the overall sector sustainability. However, it is worth noting that the inherently theoretical nature of the study somewhat limits it; therefore, future empirical research is needed to further test the proposed model, applying it to other real applicative sets.