The structure that secretes a hormone promoting the maturation of gametes is the pituitary gland.

Here's why:

* Follicle-Stimulating Hormone (FSH): The pituitary gland secretes FSH, which plays a crucial role in the maturation of both male and female gametes:

* In females: FSH stimulates the growth and development of ovarian follicles, which contain the eggs.

* In males: FSH promotes the production of sperm in the testes.

While other structures are involved in the process of gametogenesis (the formation of gametes), the pituitary gland's role through FSH is central to the maturation process.