There are multiple steps required here.

1) The two csp applications that support the Zen app and the REST app must both be defined to store their license information ( cookie ) in the same location on the browser.  You will need to make sure you have enabled cookies for sessions and that both apps put the cookie in the same location.

2) In the CSP Rest page you must tell the csp server logic that you want to use sessions. To do this you need to ovverride the parameter "UseSessions" and set this to true. This will persist the session from call to call and will look for and update the session cookie in the http request.

So you might do something like:

/csp/mynamespace as the URL for the zen app and then have /csp/mynamespace/REST for the rest calls..

Both would store the session cookie at /csp/mynamespace

This should get the same license and user allocated to both applications.