No, there is no upgrade from Office for Mac 2011 to Office 2016 for Mac, but you can install side-by-side and use either Office for Mac 2011 or Office 2016 for Mac.
It's easy to install, and there are just a few steps.
To install Office 2016 for Mac, follow the steps in Install Office on your PC or Mac.
Note: If you'd rather remove Office for Mac 2011, you can uninstall it.
Your 2011 files will not be affected by installation of Office 2016 for Mac. For information about importing Outlook data from Office 2011 for Mac to Office 2016 for Mac, see Import email messages, contacts, and other items into Outlook 2016 for Mac.