I've written exactly one synopsis, and it was/is awful. I wanted to say that, in fairness, because I have some suggestions for this fragment. I just don't know how useful my suggestions will be.I'm not sure about the wording of the first sentence. "...Falcon wants...to never wear the circlet..." This seems like a long-ish way to say, "Falcon doesn't want to wear the circlet." Both are hard starting points, because they make the character seem more interested in what she doesn't want, than what she does. Maybe you could change the wording, turn the intent around so that you are stating something positive. i.e. "All Falcon wants is to remain hidden, to stay within the safety of her false identity..."
The synopsis is a hard place to have any voice. Your second sentence seems to directly address the reader, which makes it jump right off the page. I can't say if this is a good thing, or bad, but that sentence seems to be out-of-place among the rest of the fragment, which is rapid summary.
I couldn't decide, from what you have here, if Falcon and Princess Kauril are the same person.
I didn't understand the comment about her being a spy. Who does she report to? It seemed odd that she could create such a false identity with no help at all, especially if she is a ward of the Kingdom. I guess I either need to know more about this process, or less. Who called her back? Why did she have to respond? What is she supposed to do there? spy on the Queen and King? or declare her true identity?
I don't know if you need to explain any of those things in the synopsis. However, right now I am left with so many questions that I am more confused than interested. I feel like you still haven't introduced the main conflict she will face in the book. What will happen if she is discovered before marrying and having a child? Is anyone even looking for her? Do they know her father left an heir who might someday be able to claim rule? Does she want to keep her new identity because she is afraid, or because she likes her new life? How many of these questions, if any, need to be answered in the synopsis?