I understand what the Law of Surprise is, but what if there is no surprise? In the TV series it is explained that it might be a bumper crop, or a newborn puppy but what if the giver returns to no surprise, is it carried over to the first surprise they receive, be it a birthday present or even a debt to be paid?
I'm not sure if the Law of Surprise is an actual law in any modern country in The Witcher series. It makes its first appearance in the books by the cursed human Urcheon (aka Duny, among other names), who had saved the late King Roegner's 1) life. From The Last Wish:
You know Roegner, once saved, vowed of his own will to give me whatever I asked for. /--/ ..., he asked me what I demanded and I answered. I asked him to promise me whatever he had left at home without knowing or expecting it.
Then later in the same chapter Urcheon continues to explain it:
But let us not pretend we've never heard of such requests, of the Law of Surprise, as old as humanity itself. Of the price a man who saves another can demand, of the granting of a seemingly impossible wish. 'You will give me the first thing that comes to greet you'. It may be a dog, you'll say, or a halberdier at the gate, even a mother-in-law impatient to holler at her son-in-law when he returns home. Or: 'You'll give me what you find at home yet not expect. After a long journey, honorable gentlemen, and an unexpected return, this could be a lover in the wife's bed. But sometimes it's a child. A child marked out by destiny.
The talk of destiny together with the Law of Surprise is recurring throughout the books.
Now, we know that Urcheon was very cunning and it is possible (I'm speculating here) that he knew that Calenthe was pregnant with Pavetta when he made the request to the King.
This little story has a whole lot of things going on between the lines. Calenthe is just as cunning and knew that Urcheon would appear on this day, and that he is not quite human. That's why she had hired a witcher - Geralt, who was present in disguise. Calenthe tries to dodge the King's oath in every way, but in the end she is forced to yield when Pavetta willingly agrees to leave with Urcheon - it later turns out that they had already been seeing each other romantically in secret for a while.
The situation is about to escalate in violence, since Pavetta had several suitors present at the party where Urcheon appeared. But Geralt manages to stop it and save the day - in the end Calenthe agrees that Pavetta and Urcheon will get married. Since Geralt saved his life and made the happy ending possible, Urcheon asks Geralt what reward he would want for this. Then Geralt calls upon the same Law of Surprise as Urcheon had used. And it turns out that Pavetta was pregnant with Ciri.
It's not clear if witchers also used the Law of Surprise by tradition, or if Geralt simply was inspired by Urcheon - the latter actually seems the far most likely.
Six years later, Geralt returns to Calenthe and declines to go through with the request, to take her grandchild away from her. He doesn't even know who the child is at that point. Later on, he comes across the child Ciri by chance when she has fled from an arranged marriage and got lost in the Brokilon forest. He saves her, but doesn't realize who she is.
Some years later still, during the the first Nilfgaard war against the north, Geralt calls upon the Law of Surprise once more, seemingly at a whim after saving a merchant's life and cargo. Upon returning to the merchant's home, the merchant finds that his wife has adopted a refugee child fleeing from the war in Cintra - and it turns out to be Ciri. Only then, when he adopts her, does he learn the full story, that she is the Princess of Cintra.
Geralt's two extremely unlikely encounters with Ciri is explained in the books as destiny - she was meant to end up with him, even though he had declined claiming the price. So the Law of Surprise couldn't really have ended with him getting any other price.
1) Ciri's grandfather, the husband of Queen Calenthe of Cintra.
The Law of Surprise claims something.
For example, it could be "The first thing that comes to greet you", but if nothing comes to greet you, then nothing is claimed, because there wasn't anything greeting you. But the instant something greets you, then that something is claimed by the Law of Surprise.
If it is "What you find at home yet don't expect", but you arrive at home and don't find anything out of the usual, then nothing is claimed. But someday you will return to your home and find something new or unexpected, and that something will be claimed.