Are there any examples of sovereignty in "Sir Gawain and the Green Knight" and if so what?
Yes, there are two distinct examples of sovereignty in the prose "Sir Gawain and the Green Knight".
Sovereignty, as defined by Merriam-Webster, is:
supreme power especially over a political body; controlling influence.
Therefore, both King Arthur and Lord Bertalik both have established sovereignty within their own kingdoms.
King Arthur rules his own lands- he holds the supreme power and is the controlling influence over all of those who reside within his lands.
Lord Bertalik maintains sovereignty in two different ways. First, as Lord Bertalik maintains sovereignty over the castle which he and Lady Bertalik reside. As the Green Knight, Bertalik maintains sovereignty over the Green Chapel. That being said, given Lord Bertalik and the Green Knight are the same person, basically all lands of Bertalik castle and those of the chapel are ruled by Bertalik.