What does Miss Havisham hope that Estella will do?

Miss Havisham intends to make Estella into a kind of weapon she will use in order to exact vengeance upon men. The aging lady's entire life, since having been stood up at the altar, has been consumed by narcissistic grief. She has essentially destroyed her own life, or at least completed the job that was started by the bridegroom who deserted her. Estella is a beautiful young girl whom Miss Havisham is deliberately bringing up to be self-centered, insufferably snobbish, and even cruel—to attract men and then reject them.
In the very first meeting with Pip, Estella makes fun of him when they are playing cards, saying things like "he calls the knaves jacks!" and making Pip ashamed of his working-class background. There is something both pathetic and absurd, but also understandable, about the fixation Pip develops on Estella. She keeps him at arm's length and makes him suffer, as Miss Havisham intends. In many ways, Pip's obsessive love prefigures the feelings of Philip for Mildred in Somerset Maugham's Of Human Bondage—with the difference that Mildred, unlike Estella, has apparently no positive qualities at all, not even beauty.
The ending of Great Expectations in its final version, unlike in the original version Dickens intended, has the hopeful statement by Pip that "I saw no shadow of another parting from her." It is in keeping with the overall positive message of the story that, in spite of the horribly dysfunctional situations and cruelty of many of the characters, human beings can triumph over adversity.