How to make List’s Add method protected, while exposing List with get property?

As others have said, you are looking for the .AsReadOnly() extension method.

However, you should store a reference to the collection instead of creating it during each property access:

private readonly List<SomeOtherClass> _items;

public WhatClass()
{
    _items = new List<SomeOtherClass>();

    this.Items = _items.AsReadOnly();
}

public ReadOnlyCollection<SomeOtherClass> Items { get; private set; }

This is to ensure that x.Items == x.Items holds true, which could otherwise be very unexpected for API consumers.

Exposing ReadOnlyCollection<> communicates your intent of a read-only collection to consumers. Changes to _items will be reflected in Items.