That's a great question. First, you must think on the themes which these two pieces of literature have in common. The theme most prevalent in Dickinson's poem is one of belonging/conforming and one of being shunned as an outcast or outsider. When we apply this to Dickens' novel, we come up with Pip, Estella, Miss Havisham, and Joe. All of these characters (and probably others that aren't coming to mind immediately) are treated as outsiders or people who don't belong at some point or another in the book.
Pip, though he tries to become a gentleman through education, dress, the right friends and living quarters, never quite lives up to the expectations of the one person he was trying to impress: Estella.
Miss Havisham is rejected at the alter and spends the rest of her life in a shambles of wedding attire teaching Estella not to conform, but to crush all young men in her path.
Estella, who is unable to live a normal life of a young lady who is allowed to find a young man and fall in love, get married, have children, etc. is used as the weapon of Miss Havisham. Consequently, Estella lives as an outcast even in the midst of all her wealth and beauty, she can not be like other girls in her world.
Joe, who never tries to be anything but a friend to Pip, is treated as an outcast and a source of embarrassment by Pip. This is a heartbreaking scene since Joe is such a good person and one of the only characters in the book that Pip can truly trust to have Pip's best interests in mind.
Think too, about the part of Dickinson's poem where she talks about how "dreary" it must be to live up to what everyone else expects of you...like a "frog" croaking out your name to the admiring "bog" or crowd of people who will either approve or disapprove of you. Which characters in the book fall into that category?
There are lots of wonderful similarities here...keep thinking and linking! Good Luck!