Pumblechook serves as comic relief and represents the disingenuous nature of those who admire the rich.
Here is a basic description of Uncle Pumblechook.
Uncle Pumblechook’s role is to provide comic relief. He is laughably absurd. It is clear that he is posing as more important than he actually is. He enjoys abusing Pip, pretending he is doing it for his own good. He pretends to know Miss Havisham to make himself seem important.
Pumblechook is described as a “well-to-do cornchandler” (Ch. 4). All that means is that he is a shopkeeper. Pumblechook’s greatest character flaw is that he puts on airs constantly, even around his family.
I was not allowed to call him uncle, under the severest penalties. (Ch. 4)
Pumblechook torments Pip, and seems to only like Mrs. Joe. He clearly considers himself better than Joe, and definitely thinks he is superior to Pip because Pip is only a child. He constantly tells Pip that he should be grateful to his sister for having raised him.
Pumblechook torments Pip as a matter of sport, and believes that he knows more than anyone else about any subject. The greatest example of his posing comes when he says that he can introduce Pip to Miss Havisham and pretends to know her well. Clearly he has never even seen her.
“Boy! What like is Miss Havisham?” …
“Very tall and dark,” I told him.
“Is she, uncle?” asked my sister.
Mr. Pumblechook winked assent; from which I at once inferred that he had never seen Miss Havisham, for she was nothing of the kind. (Ch. 9)
Pumblechook’s role pretty much ends after Pip develops ties with Miss Havisham. As he gets older, Pip likes him less and less, calling him a “fearful imposter” and an “abject hypocrite.” Soon Pip is much more important than his uncle. When Pip comes into his expectations, Pumblechook pretends that he cares about him and gives himself credit for everything.