Final answer:
In the game Harry Potter: Hogwarts Mystery, the character eager to access the cursed vaults in the first year is Penny Haywood.
Step-by-step explanation:
The question revolves around the Harry Potter: Hogwarts Mystery game, where players experience life as a student at Hogwarts School of Witchcraft and Wizardry. In the first year of the game, the character eager to access the cursed vaults alongside the player's character is Penny Haywood. Penny is known for her potion-making skills and becomes one of the player's closest allies in the quest to uncover the mysteries of the cursed vaults.