A legacy application does not just entail the technology that comes with it. It was developed using a particular software development methodology. In some cases, that methodology might still be in use. If the methodology used is not a modern one, such as the use of a Waterfall methodology, part of modernizing a legacy application might include changing the development approach.
The agile methodology overcomes some of the limitations of older methodologies. While traditional software development methodologies focus on a lot of up-front planning and design, an agile methodology expects and embraces change. Agile methodologies are adaptive rather than predictive. Rather than focusing on predicting the outcome, it places emphasis on adapting. It is more responsive to change, which is important in today's competitive landscape.
An agile methodology will enable your team to accomplish some of the things we have discussed to improve a legacy application, such as refactoring it by making small, incremental changes. Each sprint can be focused on particular goals to improve the legacy application.
If you are introducing microservices, an agile methodology complements that approach well. An agile approach provides a structure that will allow a development team to work together effectively. It is also particularly suited to modern build and deployment processes.