I have been trying to add a new UI Element below the "Playlist View".

But I do not know how to create a new one in the space below. I can only seem to find Replace UI Element, Cut UI Element or Copy UI Element in the context menu.

So how do I add a new one in the space below?

It's not fully obvious for me what are you trying to accomplish.
Nevertheless, to divide the area of "Playlist View" into two parts, first replace it with a "Top/Bottom Splitter", then add the second element to the bottom pane.
Try reading the Layout Editing Mode guide in HA Wiki for more information.

That is what I am looking for Yirkha.

Thank you very much.