Is there a way to \"inherit\" imports?
Example:
Common enum:
public enum Constant{ ONE, TWO, THREE }
Base clas
If you're using Eclipse, use "Organize Imports" (Ctrl+Shift+O) to let the IDE do the imports for you (or use code completion (Ctrl+Space)
imports are just an aid to the compiler to find classes. They are active for a single source file and have no relation whatsoever to Java's OOP mechanisms.
So, no, you cannot “inherit” imports
No, you can't inherit an import. If you want to reference a type within a class file without using the fully-qualified name, you have to import it explicitly.
But in your example it would be easy enough to say
public Sub extends Base {
    public Sub() {
        register(Constant.TWO, "blabla"); // without import: Constant.TWO
    }
}