Based on my past experience, there are two types of Licensing testing I have performed.
1. Phone check out/Check in
2. Internet Check out/Check in
Before involving in Licensing testing, need to understand the scope. Like, Licenses are used for a product for no.of users or no. of modules to be enabled in an application.
If it is dependent up on modules/features when a license is activated in an application, then you need to prepare a matrix template for the modules for each license and then execute based on the matrix, so that it gives maximum test coverage.
Also, you can add some of the edge condition listed below -
What if license is expired and try to activate it again?
what happens, If same user license is activated on a different PC?
Disconnect your internet connection and try to activate the license key?