Does Plesk install updates for system packages automatically?
By default, Plesk automatically updates itself and supported third-party components, but does not install all available system package updates.
In order to alter this behavior, do the following:
Go to Tools & Settings > System Updates > Settings;
Enable the Automatically install system package updates option:
Note: kernel updates are excluded from Plesk Update Manager and should be checked for manually (see the article for details).
To keep kernel updated, KernelCare Extension can also be used
Plesk Administrator's Guide: System Updates