I would recommend using mockito to mock a request to your rest endpoint with some data, and testing that your other application tries to send the correct data to the endpoint.
This way both applications are tested independently and do not have dependencies at each other. This provides the benefit of being able to substitute one of these applications with another if necessary. Also it provides a good separation. This is important because when you (or someone else) wants to use your REST application they do not use your other application so it is very important that the REST application is tested with static data written in your tests and is not dependent on the output of another application. Since REST applications are meant to be independent.
However, when you do want to test it this way you could try to include your other application in the classpath.