Booking Calendar – WordPress plugin https://wpbookingcalendar.com
Tutorial of configuration import bookings or events from other services via .ics feeds (ical links), like from Google Calendar or Airbnb, Booking.com, HomeAway, TripAdvisor, VRBO, FlipKey and any other calendar that uses .ics format.
Please read more about this feature here: https://wpbookingcalendar.com/faq/#sync
Import process is working in that case, when some visitor is open your website page with booking import shortcode. So you can configure CRON at your server, for periodically access this page with booking import shortcode to start import process. Or you can insert the import shortcode before booking form shortcode, so firstly system will start import process and only then show booking form, when someone visit your page.