What is the name of the cycle where an endocrine gland releases a hormone that stimular?

The cycle you're referring to is called a positive feedback loop. In this process, the release of a hormone from an endocrine gland stimulates further hormone release, amplifying the response. A classic example is the secretion of oxytocin during childbirth, where increased contractions lead to more oxytocin release, further enhancing contractions until delivery occurs.