I am assuming that you at least attempt to use some kind of MVC-like pattern:
The UI part does not need any changes.
The controller (servlet) needs to be injected with a web service client, to which it delegate the work. You should also remove all references to the database handler from the controller.
The database part does not need any changes, but instead of being injected into the controller, it should be injected into the web service class.
Additionally, you need to implement the web service.