If the other source is also a booking platform, using the Ical standard, then it will be done automatically at time of booking if calendars are synchronized. It is explained in this article:
Thank you Emiel for all the advice on how to best manage calendars!
@Terri604 Have you tried syncing your calendars already? A lot of hosts do it and find that it does make it easier to ensure the correct availability shows, however please let us know if this is not a suitable approach for you. 🙂