Yes. Restarts are required to update things that are loaded in memory and can’t be swapped out easily, like the running kernel.
Clear Linux will automatically restart certain whitelisted services after an update to make sure the newest software is in use but can’t do this for all services without making too many assumption about a system and potentially interrupting service. It tries to notify users that an update requiring a restart is pending.
Yes, it’s necessary to reboot to update the kernel, for example. Some services are automatically restarted on update, but others are left alone because of the potential impact (gdm, X, etc.).
You can check the MOTD for hints, though:
$ cat /var/run/motd
* A kernel update is available: you may wish to reboot the system.
* Some system services need a restart.
Run `sudo clr-service-restart -a -n` to view them.