Thanks for that info and choosing the Apple Support Communities. I know how important being able to use your VPN after updating to macOS Sierra! The good news is the following steps will be helpful in resolving your issue with Cisco Anyconnect, as they have released an update to their product to be compatible with macOS Sierra:
AnyConnect 4.3MR3 (3086) is now available with various fixes including additional Mac OS 10.12 (Sierra) compatibility fixes
If an app won't run or install on your Mac after you upgrade OS X
Cheers!
Oct 8, 2016 11:26 AM
Risks are inherent in the use of the Internet. Apple makes no representations regarding third-party website accuracy or reliability. 
Information about products not manufactured by Apple, or independent websites not controlled or tested by Apple, is provided without recommendation or endorsement. Apple assumes no responsibility with regard to the selection, performance, or use of third-party websites or products. For additional information.
Cisco Anyconnect Vpn Client For Mac Os X Yosemite
Simple to deploy and operate, the Cisco VPN Client enables customers to establish secure, end-to-end encrypted tunnels to Cisco remote access VPN devices. Free Cisco Systems Mac OS X 10.4 Intel. Step 1 Install Cisco anyconnect VPN client for Mac OS X. Double click on AnyConnect. If you see the message: “This package will run a program to determine if the software can be installed”. Citrix client for mac os x. The following is a list of user guides and other documentation related to the VPN Client for Mac OS X and the VPN devices that provide the connection to the private network. • Release Notes for the Cisco VPN Client, Release 4.0.
From Cisco Systems: