The package is called eos-update-notifier. It is already in the repos, so you may install it like any other package. A reboot is recommended after installing it.
It is a systemd service for the current user, and to see it is running, give a command
systemctl --user status eos-update-notifier.timer
It checks for updates soon after login. Afterwards it checks for updates after every two hours.
In addition, it also checks if there are any Arch news that may affect your machine, i.e. are related to the software you have currently installed in the machine. Note that this feature is usually able to show the relevant news, but sometimes it doesn’t. The reason is in the simple ad hoc method how the news are checked. So, to be on the safe side, it is still a good idea to check the Arch news (https://www.archlinux.org/news) with a browser at times.
DISCLAIMER: this piece of software is already tested but still quite new, so there may be issues. If you find a problem, please report it in the Bug reports area.