Despite of Cylance being supported on macOS 11 Big Sur since build 1580, you may encounter an issue where Cylance would still show a red dot in its icon in the menu bar, and opening the GUI would still show this error message:

Driver Failed To Connect, Device Not Protected

To resolve this, you need to give the agent and the new Cylance ES Extension full disk access:

On macOS Catalina and earlier, Cylance used kernel extensions, providing full disk access via the macOS kernel. Because of the deprecation of kernel extensions and the subsequent introduction of the new system extensions mechanism introduced in macOS 11 Big Sur, you need to explicitly allow full disk access to the system extension of Cylance.

Note about Cylance 1580

If you are still running Cylance 1580 together with macOS 11 Big Sur, be sure to update to 1584 as soon as possible. Version 1580 has a critical bug, which may cause a race condition.