Judge Arthur Vandelay is a judge for Latham, Massachusetts. He presided over the main characters’ (Jerry Seinfeld, George Costanza, Elaine Benes, and Cosmo Kramer) trial in The Finale, Part 2 where Jackie Chiles was defending the four while District Attorney Hoyt prosecuted them. When George sees the judge's name, he believes it to be a good omen, as Art Vandelay was an alias that George used throughout the series.
Art listens to the witnesses and character witnesses testify against the four; he does not have many lines.
As the jury is going over the evidence. Estelle Costanza visited Judge Vandelay's office in order to get him to reduce the punishment for her son by "doing something for him." When Judge Vandelay quotes "What do you mean," Estelle quotes "you know."
Ultimately, the jury finds the New York Four guilty. Judge Vandelay sentences them to a year in prison.