Right now, her plan was to become the Luna of this pack first. Once that was achieved, even if Zion later discovered she wasn't the real princess, it would be too late. Besides, she could always argue that she never officially assumed the title of royal princess—it was merely their assumption that led to the misunderstanding. She had just never corrected it.
No matter what, Claire believed she could talk her way out of any situation. After all, as long as she never stepped foot in the palace, there was no way Zion—or anyone else—would discover she wasn't the real royal princess.
It had already been three years since the princess went missing. So what if she used the title outside the palace? No one would question her, and no one would know she was lying.