While the paradigm of circular economy (CE) and the processes of socio-technical transition have been broadly investigated at the theoretical level, understanding how the transition toward circular models can be implemented in practice is still limited. This contribution aims to provide in-depth and evidence-based insights on an emerging pathway for the operability of CE into the olive oil supply chain. A case study from the Apulia region (the leading olive oil producing area in Italy) is presented to show how an existing business model can be transformed into a circular one, and to what extent it can be replicated. The study focuses on a vertically integrated firm, in which a new industrial process has been introduced to manage olive pomace, which is one of the most important by-products obtained from olive oil extraction. The empirical analysis is built on the Circular Business Model Canvas (CBMC), which is conceived as a suitable theoretical and methodological tool to speed up the transition process toward CE at a micro-economic level. This analytical framework allows us to identify the interplaying elements that the firm combines to capture, create, and deliver value, as well as the relationships with the broader economic system. Particular attention is paid to two distinctive components of CBMC: material loops and adoption factors. Also, internal and external factors affecting the adoption of the new circular business model have been discussed by separating drivers and barriers of the transition process.