The real problem here is that you have a base class with so many methods that a derived class can work only with a subset of them. This means that your base class most likely has multiple responsibilities and thus violates the Single Responsibility Principle (SRP).
The solution is to split your base class into several smaller classes where each of them has exactly one responsibility.
If the base class is not from you, you really need to implement all of those methods.
If the base class is a class that violates the SRP and your implementation can really work correctly if you implement only a small subset of the methods you could create an abstract base class deriving from that other abstract base class. In your abstract base class you can implement all methods you don't need and throw a NotImplementedException
. Don't implement those methods you need.
Now, derive a class from your base class - you now only have to implement the methods you are interested in. Be sure to document this properly.