You can set up a self-booking calendar so that your clients can see your availability and book meetings or request appointments during your open hours.
To do so and also keep each client's information private from other clients, you can use customized access links with a no-details permission.
Here's how it might work:
Create a sub-calendar to show your availability, and add your open times to this calendar (use repeating events to make this process easy!).
Create another sub-calendar for client bookings..
Give each of your client a customized access link with read-only permission for your Availability sub-calendar and modify-from-same-link-no-details permission for the Client bookings sub-calendar.
Each client will be able to view the details of any booked appointment they've added to the calendar, but they will only see other clients' bookings as Reserved, with no event details visible.