Incrementally migrate a legacy system by gradually replacing specific pieces of functionality with new applications and services. As features from the legacy system are replaced, the new system eventually covers all the old system's features and may has its own new features, then strangling the old system and allowing you to decommission it.
This strangler pattern is a safe way to phase one thing out for something better, cheaper, or more expandable. Especially when you want to update legacy system with new techniques and need continuously develop new features at the same time. Note that this pattern indeed need extra effort, so usually use it when the system is not so simple.