All good introductions start with a "motivator"; that is, they begin in such a way that they pique the interest of the reader.  While there are different approaches to the writing of a motivator, such as using an interesting statement, a brief story, or using a quotation, it needs to tie to the thesis of the essay.

So, you must write something that will tie to the thesis of your character analysis.  If, for instance, you wish to write how Miss Havisham has abandoned life for the "sham" [tie to her name] of the life that she leads as she instructs Estella in her revenge against the male gender, you may wish to begin with one of her famous lines such as "I know nothing of the days of the weeks, or the months of the years," or as Miss Havisham embraces Estella in Chapter XII, "Break their hearts, my pride and hope, break their hearts and have no mercy!"