Which character becomes headmaster of Hogwarts after Albus Dumbledore’s death?

Severus Snape becomes headmaster of Hogwarts after Albus Dumbledore’s death. His appointment occurs during Harry Potter and the Deathly Hallows, when Lord Voldemort’s regime controls the British wizarding government and the school.

Snape had served as Hogwarts’ Potions professor and later became Defence Against the Dark Arts professor. His relationship with Harry is antagonistic for much of the series, partly because Harry resembles his father, James Potter, whom Snape disliked from their school days.

The headmaster appointment is part of a larger deception. Dumbledore’s death was arranged with Snape’s cooperation, and Snape’s apparent allegiance to Voldemort conceals his continuing work against him. The full explanation appears near the end of the final novel.

Minerva McGonagall later leads Hogwarts during the Battle of Hogwarts and becomes headmistress after the conflict. That later role is why readers may associate her with the school’s leadership, but the immediate successor to Dumbledore during Voldemort’s control is Snape.