If you are running HA as a specific user, the chances are that the user doesn’t have sudo access. It is generally not a good idea to give the user sudo access, to prevent it being used to control your machine in the event of some successful hacking attempt.
If you want zoneminder to restart when it exits, you should investigate using the Restart=always option in the service file, which is probably in /etc/systemd/system. Try man systemd.service to see the options.
The easiest would be allowing the user hass runs under (assuming this is not root) to use certain sudo commands.
You can restrict the allowed commands/arguments in /etc/sudoers like this: