Discord on Linux does not (and **will** not) have a PPA. Drop this script in your /etc/cron.daily/ and forget about it.

update_discord

#!/bin/bash -e

echo "Are we superuser?"
[[ $EUID -eq 0 ]]
echo "OK"

# Make sure cleanup runs even if the script exits abnormally
trap "rm --force /tmp/discord.deb" EXIT

# Find latest package version
nextVersion=$( curl --head --silent --output /dev/null --write-out '%header{location}' https://discord.com/api/download?platform=linux | \
	awk -F '/' '{ print $(NF-1) }' )

# Find intalled package version
instVersion=$( dpkg-query --showformat='${Version}' --show discord )

if dpkg --compare-versions "$nextVersion" gt "$instVersion"; then
	curl --get --location --silent --output /tmp/discord.deb https://discord.com/api/download?platform=linux
	dpkg --install /tmp/discord.deb
fi