How much training does an A320 pilot need to fly an A321?
From Flight Training International:


  Airbus A320 Type Rating  
  
  
  The Airbus A320 family of jet airliners consists of five aircraft:       the A318, A319, A320, A321 jet airliners and ACJ business jet.  
  Only one type rating is required to fly these Airbus aircraft, as       they have similar flight decks.  
  To earn a type rating for these Airbus aircraft requires the    completion of a technical course that lasts anywhere from 8 to 12 days depending on your pace.
  


So the answer from a regulatory point would be no additional training.  Some airlines might have policies that require a minimal check, probably in a sim.