The access group that a new patient is assigned to depends on who has created them. If your practice wants to restrict who can view and book the patient, then you must reassign them to a different access group.
If a clinician has created the patient from the Patients page, then they are automatically assigned to all the access groups that that clinician is a part of, as well as the 'Public' access group.
If a clinician created the patient while making a new booking on behalf of another clinician, then the patient will automatically be assigned to the access groups of both clinicians.
If a user who is not a clinician has created the patient, then they are automatically assigned to any access groups that the user is a part of, as well as the 'Public' access group.