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?
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).