Thanks for your query.
Apparently it seems that you are not changing the application and only hardware/Operating system is being upgraded. In this case you just use the application as it is and place the license on the same location in new server as it was placed in old server so that license path remains valid for the application. You may please go through the following article for more details about your scenario.
If you still face some issue after upgrade, please share the details with us along with some simplest application (runnable) for our analysis. We will test it and provide our feedback accordingly.