There are certain options w.r.t. this and it is in admin's control how this can be handle.
By default, the Agent Upgrade field is set to prompt the end-user to upgrade. This behavior can be modified by choosing different available options in the agent upgrade to connect method field.
When the user connects to the client after installation of the new version on the firewall, they will be prompted with a page stating a newer version of GlobalProtect is available for download.
With this user can download and install new version on the system.
If you want to upgrade GP client version without interacting with user, select the "Transparent" method in the app configuration. This setting will automatically upgrade agent on clients system.
I think, second method will help you to achieve your use case.
Hope it helps!
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