Simpson will take over the role following Denise St. Pierre's 31 years of leadership.
As Singleton prepares for the 2023 season, he first wraps up his second offseason of NIL partnerships.
Carter received an offer from Rhoades just 10 days ago and will be the first piece in the Nittany Lions' recruiting Class of 2024.
Pickett will don No. 24, while Lundy will rep No. 8 on their respective NBA teams.
The Nittany Lions will play 17 series, with eight of them hosted at Pegula Ice Arena.
Tickets can be purchased beginning at 10 a.m. on Friday, June 30, though several presale promotions will kick off on Wednesday, June 28.