Possible Clues:

• A pontiff
• Fish, as fisherman's successor
• Alexander - - , brilliant satirist of the Augustan period
• Predecessor or successor of Alexander
• The most recent one was inaugurated in 2005
• Fish served in the Vatican
• 'An Essay on Criticism' essayist
• John or Paul but not George or Ringo
• Tiara wearer
• A poet at the Vatican