Whereas Outlook for Mac 2011 doesn’t support the archive feature, Outlook 2016 for Mac does support the archive feature. When you use Outlook 2016 for Mac, you can access your archive and move mail items into your archive.
You can create an archive mailbox for a user's primary cloud-based mailbox. Users can use the archive mailbox (also known as a personal archive) to store historical messaging data by moving or copying messages from their primary mailbox to their archive mailbox. The archived messages reside in the cloud, and users can access the messages by using Outlook 2016 for Mac, Outlook 2013, Outlook 2010 or Outlook Web App.