They go back to their routine. Vanyel reads about magic and practices magic and eventually consents to let one of Leareth's employees, a Mindhealer who's also a mage, have a look at his Gifts and see if she can help. He makes faster progress.
They sing and spar and Vanyel gets back in shape and learns more of Tarinda's fancy combat-dance techniques. (It's not like his swordfighting style has to be practical, real fighting he does with magic.)
It takes Savil and the Tayledras a month to figure out moving the Heartstone, during which Vanyel stays up north. He does go back to Haven afterward, but he asks the King about visiting sometimes, he likes keeping Tarinda company and also at this point he's not really needed for Valdemar's security, none of their borders are at risk including the north, and it seems pretty valuable to learn magic from Leareth and Leareth's library?
The King agrees he can alternate weeks in each place, if he wants, since Leareth apparently has lots of people who can Gate him back and forth.