After answering all the questions Clair runs in and they have a chat; she gives you the Rising Badge and leaves. Go to leave the Dragon Den and you'll find Clair near the exit. Talk to her for a bit and she'll give you her TM. Go back to see the Elder and he'll give you the Dratini. I've heard reports of ExtremeSpeed being the last move Dratini has, replacing Dragon Rage. My Dratini had ExtremeSpeed replacing the first move, replacing Leer I believe.
Thanks for reading, and enjoy your new Dratini!