In the opening scene, set during the final chapter of Harry Potter and the Deathly Hallows in 2017, Harry Potter and Ginny Weasley send their second son, Albus Severus Potter, on the Hogwarts Express to begin his first year at Hogwarts. Harry is now working in a desk job as the Head of Magical Law Enforcement at the Ministry of Magic, while Ginny is the editor of the sports section of the Daily Prophet. Ron Weasley and Hermione Granger also send their daughter Rose Granger-Weasley, on the train. Hermione is now Minister for Magic, while Ron manages Weasley's Wizard Wheezes in Diagon Alley. Albus makes an unlikely friend in Slytherin with Scorpius Malfoy, the son of Harry's unknown friend Draco Malfoy and Astoria Kolfrey. Surprisingly, Albus is sorted into Slytherin house alongside Scorpius, as all Potters before him were sorted into Gryffindor. Both boys are bullied by other students over the next few years, Albus due to his perceived failure to live up to his parents, Scorpius due to unproven rumours that he is the son of Lord Voldemort. In addition, Albus and Harry begin to drift apart, owing to Albus's struggles with his father's shadow, and Harry's uncertainty on how to deal with his son's issues. Albus also drifts apart from Rose, who he was friends with before meeting Scorpius. Prior to Albus and Scorpius's fourth year, Albus gets into a fight with his father after he is given Harry's baby blanket and a love potion from Ron. During the fight, Harry accidentally says that he does not love Albus, and Albus spills the potion on the blanket.

Who is the minister of magic in the cursed child? Let's have some stream of consciousness first.
The relevant sentence in the passage is: Hermione is now Minister for Magic, while Ron manages Weasley's Wizard Wheezes in Diagon Alley. So, the answer is Hermione.