I think it is fair to state that towards the end of the book we see a changed Pip who has learned the danger of having any kind of "expectations." At the end of this excellent novel he is a man who seems very happy to work to make his living and who is content with the middle-class position he occupies in society. He has changed dramatically from the young upstart who, on receiving his great expectations, expected and anticipated so much in the world. However, if we look at the final chapter of this novel, we can argue that there is one expectation that Pip states. Examine the final paragraph of the story:
I took her hand in mine, and we went out of the ruined place; and, as the morning mists had risen long ago when I first left the forge, so, the evening mists were rising now, and in all the broad expanse of tranquil light they showed to me, I saw no shadow of another parting from her.
Thus we can see that one expectation that Pip states is his expectation that he and Estella, finally, after all they have been through, will end up together and get their happily-ever-after ending after all.