I recently switched my desktop from Gnome to Xfce. Xfce does not have a panel update notifier like Gnome. You can roll your own using apt commands and cron.
Normally I would use the cron parameter @reboot but this may not work correctly to send mail depending on how long it takes to establish your network connection on bootup. It is easy however to pause execution to prevent this problem using the sleep command:
@reboot /usr/bin/sleep 120 ; /home/mike/scripts/apt-check.sh
Script apt-check.sh:
#!/bin/bash
# This code is wrapped in process brackets so all commands can be sent to mail
# This script needs to be run as sudo or from root's crontab
{
echo ""
echo "Updating Package List"
echo "-------------------------------------"
apt-get update
echo ""
echo "List of Available Apt Upgrades"
echo "-------------------------------------"
apt list --upgradeable
echo ""
} | mail -s "INTEL-NUC Available Apt Updates" mike@sierraai.com