Yes, we can override that method which throws NullPointerException in superclass and throws Runtime Exception in subclass.
Here is an example:
void method() throws NullPointerException
class Second extends First
void method() throws RuntimeException
One of the most important thing is, When you override any method in subclass, that method never throws any checked exception.The overriding method can throws any checked/Runtime exception.
Overridden method in Java shares same name as original method in Java but can only be overridden in sub class. Original method has to be defined inside interface or base class, which can be abstract as well.
When you override a method in Java its signature remains exactly same including return type. JVM resolves correct overridden method based upon object at run-time by using dynamic binding in Java.
Overloaded method can be subject to compile time binding but overridden method can only be bind at run-time. Static method can not be overridden in Java.