From A Wiki of Ice and Fire
At some point between the ending of The Hedge Knight and the start of The Sworn Sword, Dunk and Egg reached the Prince's Pass in Dorne, probably seeking Tanselle Too-Tall as hinted by the last few words of The Hedge Knight. Dunk's horse, Chestnut, died on the crossing from the Prince's Pass to Vaith. He and Egg rode double on Thunder for an unspecified period of time until one of Egg's brothers gave them Maester (it is not as of yet known whether it happened before or after reaching Vaith). Once in Vaith, Dunk met the aged Lady Vaith and spoke to her with such lack of grace as to put his own life and Egg's in danger. According to Egg, however, Lady Vaith was mad, so it is unclear if that danger could have been avoided.