Possible Clues:

• It's up to the artist to be the one to use his teeth to settle the dispute
• To get the Academician up, the judge may have to get his teeth into it at last
• Judge - mediator
• See second point in argument and bear it out? I might
• Mediator, referee
• Snapper taken from a river by expert
• Judge arrived, carrying a little to eat
• Umpire arranged to eat snack
• Controller arrives, having eaten a little something
• As a referee, an artistic back biter