If you are running the Long Term Service Branch version of Windows 10 Enterprise, you will be able to download the latest version October 1st, then perform a repair upgrade. If you are not connected to Domain, you should be able to upgrade to Windows 10 Enterprise using Windows Update. If you have a MSDN subscription, you can also manually download the ISO from there then perform a offline upgrade. Volume License clients such as Windows 10 Pro and Enterprise/Education utilizing KMS and MAK licenses should be updated by downloading the installation files for Windows 10 from the volume license servicing center. How to upgrade to Windows 10 Enterprise 1607
This is especially the case if you are connected to a workplace/school/domain. The ability to upgrade Windows 10 Enterprise will depend on your employer and Network/IT Administrators discretion.
With the release of the Anniversary Update, Microsoft has also provided an Anniversary Update for Enterprise licenses. In addition to the Windows 10 Home and Pro editions Microsoft also provides a volume license client for large organizations such as schools, governments and businesses who deploy Windows 10 in bulk, called Windows 10 Enterprise.