"We thank Elisabeth for her contribution to our Board discussions and wish her well in the future," the company's chairman Stuart Chambers said.
Brinton took her position on the board in March of last year. She also served as executive vice president of global renewables and energy solutions at Royal Dutch Shell from April 2020 to February 2022.
At the time of her appointment, Chambers flagged her experience in developing clean energy strategies, with a commercial focus on the potential for digital technologies, as a key addition to the board.
Anglo's share price dropped 6% day on day to close the 23 September session at £26.70 (US$27.76).