While Zeta was doing the very important task of tracking all the enemies before the start of the main hunt, the other ladies were also not slacking off.
Rosalie was brought here to the Otrefiona Empire as a future asset and the emperor had already accepted her as one. Normally a mage of her calibre would join the royale ministry of Magic but that did not happen for Rosalie.
Instead, she was a given a special position under Azusa's supervision. Even though Azusa was currently absent, her authority was still intact as her disappearance had not been declared to the public.
So with the help of that authority, Rosalie was given the position of head researcher of Magic Research and Development centre. This was something brand new that the emperor and Azusa had created for Rosalie. In the future, she could find more people to work in this orginisation.
