Amplenote does not yet offer direct integration with Apple Calendar, however you can still establish a sync between the two using Google Calendar as an intermediary. By connecting a Google Calendar to both Amplenote and Apple calendars, Amplenote calendar entries get pushed to Apple and vice versa. Here's the two part process to set it up:
Connect your Google Calendar to Amplenote
Connect your Google Calendar to a Task Domain
Select "Show events and publish tasks" to enable two-way sync
Note: Events created on your Apple Calendar need to be assigned to your connected Google Calendar account, which is typically not the default calendar. You can change the default calendar for events by going to Calendar > Preferences > Default Calendar
Once set up correctly, all applicable tasks/events will appear on Amplenote, Google, and Apple calendars.
Task created on Amplenote (left) and edited on Apple Calendar (right)