IIRC, it was originally a short story, but New Spring was also later published as a novel in its own right. It was to be the first of a trilogy, leading up to the events in TEotW.

It was the Keeper's Foretelling. It can be found at the bottom of page 36, hardcover, in chapter two, A Wish Fulfilled. She then died in Moiraine's arms and the Amyrlin then swore Siuan and Moiraine to secrecy, being told to lie if the had to, even to another sister.

A short time later, Siuan and Moiraine were raised to sisterhood, and shortly after that, the Amyrlin, along with sisters that she had contacted after the Keeper's death mysteriously died, (i.e. were killed by the Black Ajah.) It was the death of the Amyrlin and the other sisters that revealed the existence of the Black Ajah to Siuan and Moiraine.

With those deaths, the two also realized that they were the only people left alive that knew that the Dragon had been reborn. At least the only two that knew this, and that they knew could be trusted, since anyone else with the knowledge was surely Black Ajah.