Hey Coral Star, this instance happens in chapter 7, when the player gets to choose Asterion's fur color. You can ask Asterion what fur color he'd prefer. If you've been good to Asterion you get the option to tell him you won't hurt him. Pick this. If you've been VERY good to Asterion up to that point and promised not to send him to the valley again, you will pet him.
Later on, in chapter 12, if you never sent Asterion out and have been, again, nice to him throughout the game, you get to hug Asterion before his lyre performance.
Hope this helps!