In Great Expectations, how does Pip display characteristics of a dynamic character?
Great Expectations is all about Pip's being a dynamic or developing character. It is part of the Bildungsroman genre which means that it is the tale of a character's maturation process.
Pip's name means "seed," and indeed, as readers meet him in the first chapter, he is an innocent boy untouched by society's manipulation. As the plot develops and Pip meets Miss Havisham and Estella, learns of a mysterious benefactor, moves to London, squanders his money, shuns friends, and finally realizes redemption, we see Pip change from someone who places great importance on appearance and social status to a true gentleman who recognizes the significance of family, loyalty, and kindness.
I assume you mean "dynamic" in the sense that he undergoes some major change in his personality or the way he sees the world. I believe Pip has at least two major changes in his personality.
First, when he gets rich or gets to be a gentleman, he gets to be kind of stuck up. He used to be nice and friendly with Joe and now he wants nothing to do with him because he's poor.
Second, quite late in the book, Pip sort of turns himself around. He starts caring about Joe again and goes back to being more like how he was originally.