This is currently available in TheraNest, you may just need to enable this setting under the Organization tab.
Click the "Organization" tab.
In the left sidebar, click "Client Portal"
Make sure you're on the "Settings" tab
Under "Client Notification Settings", check the box next to "Creates an appointment"
This will send the client an email notification when an appointment is created in TheraNest. Here's more information: https://theranest.zendesk.com/hc/en-us/articles/360051577812-Manage-Client-Portal-Appointment-Notifications
Thank you!