Some agencies provide an iCal link, some do not, and the answer differs.
When there is a link
Look in your owner area for "planning", "availability" or "synchronisation". The link ends in
.ics. Paste it into Calendar → Add an external calendar, and name it after the agency —
you will be glad of that when you have four.
When there is none
Either block the dates by hand each time the agency books, or decide your website is the source of truth and send the agency your availability yourself.
Paper bookings
A booking taken by phone or post appears in no calendar. Enter it as soon as it is agreed, even without a deposit: it is the leading cause of double bookings, well ahead of technical problems.