At first I thought it was McGonagall, but I didn't really recognize this woman in the left corner. What is her name and role in the movie?
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That, is Madam Irma Pince (or generally addressed in the books as Madam Pince). She is the librarian at Hogwarts.
Her description, collected across the HP books:
One of Madam Pince's most striking physical attributes was looking like an underfed vulture. She was also very thin and irritable-looking.
Harry Potter and the Chamber of Secrets: Chapter 10 (The Rogue Bludger)
According to IMDB, Sally Mortemore is mentioned to be playing the role of Madam Pince. Per her IMDB page,
Additionally, from the film, below is a screenshot of the end credits supporting IMDB's claim.
So, the person in question is undoubtedly Madam Irma Pince (played by Sally Mortemore).