The Gryphon’s Lair by Kelley Armstrong

Rowan is now the Royal Monster Hunter, and her twin brother, Rhydd, is destined to be king. But her mother’s cousin Heward is still determined that his children be the ones to inherit the titles, and will stop at nothing to show that Rowan and Rhydd are too immature to properly lead. After the gryphon that Rowan captured in Book One gives birth but then dies, Rowan is left with a baby gryphon she knows she cannot keep. And it grows faster than anyone can imagine . . .
In order to save face after an accident involving the troublesome gryphon, Rowan, with the help of her friends Dain and Alianor, along with an entourage of monstrous companions, must make a journey to the mountains to release the gryphon back into the wild. What starts off as a simple enough task soon becomes a dangerous quest, as the group encounters numerous rare and deadly monsters along the way, including wyverns and ceffyl-dwrs. Nothing is easy when you’re a “monster magnet” like Rowan.
Can she prove herself worthy of the title of Royal Monster Hunter?