The 27-year-old Hosking missed most of last season due to an ankle syndesmosis injury but appeared in 23 games for the club in the past three seasons.
Before moving to the Tigers, the popular cult hero played with the Carlton Blues AFLW for five years, managing 30 matches played.
The club have also confirmed that forward Stephanie Williams will not return to the club.
Williams entered the club after being traded from the Geelong Cats in 2022 and would play five games in her debut season at the club before a strained ACL derailed her.
Kate Sheahan, the Head of Women's Football at Richmond, spoke on the departure of the duo and wished them well for their following chapters in the future.
“I would like to thank Steph and Jess for their hard work and passion during their time at Richmond,” she said in a club statement.
“Jess brought a lot of experience to our program and played her part in some strong periods for us, including featuring in both of our finals last year.
“Steph brought a lot to our football program and broader Club and even while inactive on our playing list in 2023, Steph has remained engaged and supportive of the team.
“We wish them both well.”