That voice belonged to Elayne Trakand, Daughter-Heir of Andor. Her brother, Gawyn, is there with her. After Elayne bandages Rand’s head injury, their half-brother Galad shows up to shit all over their fun. Hearing of the stranger in the palace grounds, Queen Morgase demands to see all three of them. Elaida is at the Queen’s side, eager to tell everyone what a shifty character Rand is. Fortunately for him, Morgase believes his story and allows him to leave the palace grounds.

The book is pretty clear about Elayne’s appearance.
The voice that startled Rand off of the wall belongs to Elayne Trakand, Daughter-Heir to the throne of Andor. Yep, we’re in chapter 40 of 53 — seems like the perfect time to introduce a new major character, if your name happens to be Robert Jordan. Elayne’s mother has ordered her to stay away from the Logain business, but curiosity wins, so she dragged her brother Gawyn out of the palace for an adventure.

Galad’s role model.
Elayne bandages Rand’s bleeding head. Following introductions, Rand realizes he’s in deep shit. Not only has he entered the palace grounds without permission, but he is also in the company of the royal children. At this moment, Galad — Elayne and Gawyn’s half-brother — discovers them. We’re told that Galad is a very just person who never lies and always does what’s right. But he comes off more as a pedantic, snide, self-serving weasel who enjoys ruining everyone else’s day just because he is so pathetically unlikable that nobody wants to be around him — in other words, Galad makes a first impression that is identical to Arnold J. Rimmer from Red Dwarf. And frankly, Rimmer might be more fun at parties.
Thanks to Galad, Elayne, Gawyn, and Rand are marched into the palace to stand before Queen Morgase. Elaida is there too, and she is knitting as though she is a harmless spinster sliding into her golden years. Bitch, let me tell you something: you aren’t fooling anybody. My cat likes to make a show of innocence as well, but that doesn’t stop her from scratching the couch, puking on the rug, and knocking shit off the counter the very next chance she gets.
When the conversation turns to Rand, Elayne argues that interacting directly with citizens of Andor is the best way to come to know the Queen’s subjects. Elaida takes a level of interest in Rand that makes him understandably uncomfortable. She talks about how unusual his physical attributes are for a Two Rivers native, and she discovers that the sword at his waist carries the heron mark. At this, the entire room tenses up. The heronmark sword is the sign of a master swordsman. Nobody in the room is ready to believe it really belongs to Rand until Gareth Bryne, the Captain-General of the Queen’s Guard, pronounces that it fits him so well that it must belong to him.
We then learn that Elaida has the gift of Foretelling. Oh, Elaida — that’s a difficult gift to have, you know. Remember what happened to Gitara in Chapter 2: A Wish Fulfilled from New Spring? Yeah, that was the one where the Amyrlin Seat’s Keeper of the Chronicles felt the rebirth of the Dragon, warned everyone about it, and promptly dropped dead. Fortunately for Elaida, she seems to have a better handle on the talent. She spews a bunch of doom-and-gloom about darkness swallowing the world. Then she cranks up the creep-factor, leaning in close to Rand and whispering to him alone that big changes are coming to the world, and he is the center of it all.
Elaida and Gareth suggest that Morgase throw Rand in jail for a while, but Morgase disagrees. She says that suspicion is smothering Andor, and she won’t be a part of it. Rand swears an oath that falling into the palace grounds wasn’t part of some plot, and she sends him on his way. Elayne and Gawyn come along to the gate. Elayne tells him he’s handsome. Gawyn says he looks like an Aielman. Congratulations, Rand — that makes you exotic eye candy.