The category “organization context”, its definition content, components, and structure according to the international standard ISO 9001:2015 are reviewed. A significant discrepancy between the concepts of the organization “context” (which is contained in the original version of the standard) and “environment” (adapted Ukrainian translation of the standard) was identified. Methodical approaches and tools for evaluating and updating the organization context are proposed: SWOT analysis, PESTEL methodology, and “7S model” in particular. Considering the lack of strict regulation and requirements for specific methodical approaches to determining the context in the ISO 9001:2015 standard, ample opportunities to choose the most optimal and convenient assessment tools are indicated for organizations. The concept of “contextual ambidexterity” for organizations is introduced and substantiated, which is understood as the ability of an organization to balance simultaneously between constant adaptation to the constantly changing external environment conditions and ensuring stable parameters of current business processes. It is emphasized that the organization context is not only an element of QMS that requires constant attention in terms of formation and updating, but it also has a crucial part in the process of forming a general quality culture and has a significant impact on productive efficiency indicators (both individual and collective). The place and role of the QMS and, especially, the category of the organization context are defined in the post-war reconstruction of Ukraine as one of the pillars and levers that provide additional opportunities and create the basis for the activating of internal adaptation mechanisms, the formation of economically proven strategic guidelines for development, motivation, and involvement of the team to create a valuable product.