Ask HN: What is your process for Java application modernization?

I've recently joined a consultancy and a big part of the work is helping clients to level up extremely old apps. Other typical tasks include replacing old SOAP calls with newer HTTP/JSON microservice calls.

For a flavor of what I'm talking about a typical Java app is written in Java 6, is built via Ant and is manually deployed to machines in a private data center. There are no existing tests. Many of the library dependences are unversioned and the jars are checked into the version control system.

How would you approach the process of modernizing these apps?