The first character that comes to my mind when I think of static characters in this novel is Orlick. Throughout the course of the novel, from when he works at the forge helping Joe to when he tries to kill Pip towards the end of the novel, he remains a bitter, evil individual who has few redeeming qualities. He is a character who is shown to bear a massive grudge against Pip because of his good fortune and the way that he is loved by Joe. Orlick is also responsible for the attack on Mrs. Joe, which significantly he carried out with the leg irons of an escaped convict tha the found in the marshes. This represents another link between Pip and crime, as these were the irons that bound Magwitch that he was able to release himself from thanks to Pip's thievery of Joe's file.
As for other static characters you might like to consider Jaggers and Bentley Drummle, the "spider," as he is affectionately referred to by Jaggers. These are two other major characters who are marked by their lack of dynamic qualities: they stay the same throughout the novel.