Judge Arthur Vandelay is a judge for Latham, Massachusetts. He presided over the trial of the "New York Four" (Jerry Seinfeld, George Costanza, Elaine Benes, and Cosmo Kramer) in The Finale, Part 2. Jackie Chiles was defending the four while District Attorney Hoyt prosecuted them. When George hears 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 visits Judge Vandelay's office in order to get him to reduce the punishment for her son by "doing something for him." When Judge Vandelay asks "What do you mean?", Estelle says, "You know." The episode ends without revealing whether either Estelle or Vandelay in fact knew of any useful service she could perform for him, or if Vandelay agreed to her proposal.
Ultimately, the jury finds the New York Four guilty. Judge Vandelay sentences them to a year in prison.