How to renew expired self-signed trusted device certificate for 10.x?

In version 10 the same certificate from the GUI (Configuration Utility) is used for HA communication, in v11/12 there are new certificates for that.

You can renew the certificate just going to the certificate and use the renew button. Based in the solution for that, you don't need to do anything related with the HA config. Anyway try to do a config sync after to make sure things are working.

Solution that explains the certificates used in v10:

https://support.f5.com/kb/en-us/solutions/public/8000/100/sol8187.html

Solution that explains how to renew a self-signed certificate in v10:

https://support.f5.com/kb/en-us/solutions/public/7000/700/sol7754.html