The most obvious way to write an essay about revenge in Great Expectations would be to focus on Miss Havisham and the way she ruins lives in her quest for vengeance. When Pip meets her, Miss Havisham has not recovered from being left at the marriage altar. Her diminished life is motivated by her desire to destroy a man by having him jilted the way she was jilted. She raises her ward Estella to be cold, haughty and rejecting so that she can achieve her revenge through Estella. She shows little regard for Estella's needs or what being raised as a cold-hearted woman will do to her. Pip becomes Miss Havisham's victim: he is to fall in love with Estella and have his heart broken. Miss Havisham is also an unintended victim of her own scheme, trapped in a destructive cycle brought on by a past she can't escape.
To write such an essay, it would be best to gather quotes about revenge from the novel, and quotes about how Miss Havisham's revenge scheme impacts other characters in the novel.