Inheritance with Singletons
If the objective is to avoid duplicating information in memory, the code you have given won't archive it.

The new keyword hides the original value. It doesn't replace it. You should try another approximations, like the Decorator pattern: https://en.wikipedia.org/wiki/Decorator_pattern

The MasterData inherits from the GlobalData class and stores internally the reference to that class. Whenever someone accesses to a property of the GlobalData class, you redirect the request to the instance stored internally.

The MasterData class stores only the values of the newly added properties.

The tricky part would be preventing other parts of your MasterApplication app calling to the GlobalData class and thus creating another instance.

Singletons are always a nightmare...