Closing Long-Empty Accounts Now Act of 2013 or the CLEAN Act - Directs the Council of the Inspectors General on Integrity and Efficiency to submit a report that: (1) lists each U.S. government bank account that has a zero balance for 180 days or more, and (2) recommends which of such accounts should be immediately closed. Requires the appropriate agency to close each such account recommended for closure not later than seven days after the report is submitted.