You need to have more than one staff record to see this feature, or else new customers will see no staff to book with. Alternatively, you could stop new customers from booking online.
To hide a staff member from new customers, within Settings > My Business, click the pencil (edit) button against their record followed by [Hide _ from new customers]:
Set a cut-off date for new customer registrations and click [Save] at the bottom of the form:
You can see when a customer registered on their record page:
If you have Cancellation Watch enabled, a new customer that signs up to it without preference for a staff member can receive notifications for appointments with hidden staff and be able to book with them.
The purpose is to maximise productivity by helping to fill last-minute cancellations as soon as possible, regardless of whether the staff member is hidden from the new customer.
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How to stop new customers from booking online - Prevent new customers from making appointments and control which ones to allow through.