The Teleport Access API provides a simple Discord access request plugin that sends an alert to a Discord channel when an access request is created. You can find the Teleport Access API in the main Teleport repository and the Discord access request plugin in github.com/gravitational/teleport/api/integrations/access/discord.
If you have a self-hosted Teleport deployment, you can find information for configuring this access request plugin in Access Requests with Discord.