Gully has placed a request for the Survey Corps to assist with, having something to do with Nosepass.
The Request
Check on the blackboard in Professor Laventon's office in Galaxy Hall in Jubilife Village to accept this request.
Go to Highlands Camp
Go to Highlands Camp in the Coronet Highlands and talk to Gully.
Go to Wayward Cave
Go northwest to Wayward Cave and go inside. Find Gully and talk to her to give her a Nosepass.
Reward
You will get 1 Black Augurite and 2 Exp. Candy M.