Before you start...
Apple requires two-factor authentication and an app-specific password to connect to third-party applications like Calendly. The app-specific password is different from your standard Apple password and is unique to Calendly.
Before connecting your iCloud calendar in Calendly, retrieve your app-specific password from Apple:
Sign in to https://appleid.apple.com/.
From Security, turn on two-factor authentication (if you have not done so already).
Under App-Specific Passwords, select Generate Password.
Enter a password label (for example, "Calendly"). Select create.
Copy the app-specific password, then select done.
In Calendly, select Account, then select Calendar Connections.
Select Add Calendar Account.
Next to iCloud calendar, select Connect.
Enter your iCloud email address and paste in your app-specific password.
If you'd like to make any changes, select Edit in the relevant section.
From Edit, only the calendars native to your iCloud account will show.
Note: If you use Apple Calendar (iCal) to view calendars from other calendar services (like Google or Exchange), you'll want to connect the other calendar service directly to Calendly by selecting + Add Calendar Account.