Modern projects are implemented in conditions of high uncertainty and a dynamic external environment. Project managers should respond promptly to unexpected changes in requirements, market conditions, and other factors. This article addresses the issue of enhancing adaptability in project management. It presents a literature review on the integration of change management with project management as well as a comparative analysis of traditional and agile methodologies. It is demonstrated that conventional approaches are insufficiently effective in environments characterised by frequent changes, whereas agile methodologies significantly increase project success rates by enabling rapid adaptation to new conditions. Based on best practices, an original algorithm – FASTADAPT – is proposed: a nine-step sequence for project managers designed to facilitate systematic responses to unforeseen changes. The stages of the algorithm are described in detail, and recommendations for its practical implementation are provided. Using real-world case studies, it is shown that applying FASTADAPT reduces response time to change by 30–50%. The article concludes by highlighting the advantages of the proposed approach in increasing project resilience to external influences. It also outlines current limitations and suggests directions for future research, including the need for empirical validation of the effectiveness of FASTADAPT across various industries.