Private Sessions has a built in integration with Simply Schedule Appointments.
Activation
First, simply upload and activate any plan (free or paid) of Simply Schedule Appointments.
Once active, you’ll have a new setting within Private Sessions (accessible at LearnDash > Settings > Private Sessions) to allow students to schedule an appointment.

Configuration
Once activated, any user who’s not an administrator or group leader will have the ability to schedule an appointment based on how you’ve configured Simply Schedule Appointments.
Appointments are scheduled through an active session, through the “Schedule Appointment” tab.

We recommend you review the Simply Schedule Appointments documentation to learn how best to setup your appointment availability and options.