How to make this code fit into the base class
You can create an abstract method that will wrap the GetXXXAsync() method:

public class BaseClass&lt;T&gt;
{
    protected void Getitems()
    {
        // some preparation code here which is the same for all sublcasses

        GetItemsInternal(a =&gt;
        {
            // same code here for all sublclasses
        });
    }

    // probably needs a better name
    protected abstract void GetItemsInternal(Action&lt;EntityResultArgs&lt;T&gt;&gt; operationComplete);
}

public class DerivedClass : BaseClass&lt;SomeType&gt;
{
    protected override void GetItemsInternal(Action&lt;EntityResultArgs&lt;SomeType&gt;&gt; operationComplete)
    {
        _model.GetXXXAsync(operationComplete);
    }
}