No. private
would mean that nobody could use it, which is not sensible.
An interface can be an extension of another interface (but not an extension of a class):
public interface ExciseTaxable extends Taxable { double extraTax = 0.02; double calculateExtra(); }
A complex hierarchy of interfaces can be constructed using this feature. This is an advanced feature which you will probably not need to use.
Can a class extend an interface?