Override abstract readonly property to read/write property

You can’t do it directly, since you can’t new and override with the same signature on the same type; there are two options – if you control the base class, add a second property:

public abstract class Base
{
    public int Property { get { return PropertyImpl; } }
    protected abstract int PropertyImpl {get;}
}
public class Derived : Base
{
    public new int Property {get;set;}
    protected override int PropertyImpl
    {
        get { return Property; }
    }
}

Else you can introduce an extra level in the class hierarchy:

public abstract class Base
{
    public abstract int Property { get; }
}
public abstract class SecondBase : Base
{
    public sealed override int Property
    {
        get { return PropertyImpl; }
    }
    protected abstract int PropertyImpl { get; }
}
public class Derived : SecondBase
{
    public new int Property { get; set; }

    protected override int PropertyImpl
    {
        get { return Property; }
    }
}