Are there any examples of sovereignty in Beowulf or Sir Gawain and the Green Knight? If so, please explain.
Sovereignty is defined in many ways. Today it is defined as a supreme ruler or one possessing power. Historical definitions include in its meaning very good or effective. Based upon what definition is used, one could support the existence of sovereignty in both Beowulf and Sir Gawain and the Green Knight.
In Beowulf, regardless of what definition is used, one can find sovereignty. Hrothgar is king of the Danelands, and Beowulf, upon his return to the Geatlands after defeating both Grendel and his mother, becomes king. Therefore, both would be considered the supreme rulers of their lands.
In Sir Gawain and the Green Knight, Sir Gawain serves under King Arthur (his sovereign). That said, if one were to apply an earlier definition of the term, he or she could support that he is sovereign (based upon him being very good or effective). He is very good given he keeps his promises to Bertilak (the Green Knight). Also, he is effective in keeping his promise to be at the chapel when he is supposed to. Outside of that, the tale does contain two different leaders, Arthur (king) and Bertilak (the lord of his castle and land). Both could be considered sovereigns.
A sovereign power has absolute sovereignty if it has the unlimited right to control everything and every kind of activity in its territory. This means that it is not restricted by a constitution, by the laws of its predecessors, or by custom, and no areas of law or behavior are reserved as being outside its control.
So, if you read Beowulf or Gawain - did you see anything like that in what you read?