Hi Connor:
This is an interesting issue. Either your 2 swans laid new eggs and the third swan is so young that it is sitting on the nest just to be sitting, or your birds are completely finished with nesting this season and the new bird was looking for a quick place to lay eggs. Maybe, something happened to her mate and she saw the nest and took the opportunity to lay eggs.
The first scenario does not make sense because your birds would be protecting the nest and fighting with the new swan.
The second scenario is weird, but could explain what you are seeing. If the new swan is very young and lost her mate, she could be laying eggs, but may or may not incubate the eggs to fruition depending on her age and experience. In this case, if new cygnets are hatched, there may be a fight between the adults for territory of the pond unless it is a large pond that supplies everyone with ample space.
A third possibility would be that your swans know this bird. Could it have been one of their previous cygnets? Some swans do allow swans they know to come back to the habitat.
Please keep us updated on this interesting situation. The Regal Swan