In Chapter 23, Pip visits the Pockets' home with his new friend Herbert. The narrator mentions that when Mr. Pocket was young he was "not quite decided whether to mount to the Woolsack, or to roof himself in with a Mitre."
A footnote in the Norton Critical Edition of the novel explains that the "Woolsack" is the cushion sat upon by the Chairman of the House of Lords, and that the Mitre is the tall, peaked hat worn by the Pope. In other words, Mr. Pocket had his own "great expectations" for his future career.
Dickens, Charles. Great Expectations. Ed. Edgar Rosenberg. New York: Norton, 1999.
Pip’s apprenticeship is paid for by Miss Havisham but he is not satisfied with his prevailing situation which is made worse by his wish to become a gentleman so he can marry Estella, Miss Havisham’s daughter. A convict he helped once becomes Pip's benefactor and eventually he is able to make a trip to London to become a gentleman under the tutorship of Mr. Mathew Pocket. Mathew Pocket is coincidentally a relative of Miss Havisham and Pip develops a friendship with Mr. Pocket’s son Herbert. On arriving in London, Pip meets with Herbert and his family and he later meets Mr. Pocket who is pleased to meet him. During the meeting it is established that Mr. Pocket in his youth was undecided on whether to become the Lord Chancellor/ judge or to become a bishop. This comes out in Mr. Pocket’s description: “not quite decided whether to mount to the Woolsack, or to roof himself in with a mitre.” A woolsack is a traditional seat for judges while a mitre is a headgear used by bishops during religious ceremonies.