This can be caused by a conflict with some other event in your google calendar or some other event in your calendly itself.
Make sure there are no other events at the same time by going to ADMIN View in calendly.
Check the Video directly from calendly for more : https://help.calendly.com/hc/articles/223145627
Your calendar may already have a "busy" event at that time
A setting within your event type may be blocking your availability
Log in to your account and view any of your live event type pages. By default, you’ll see the public display of your availability shown to invitees. Locate the toolbar at the top of the page and click View as invitee. Update the setting to see an admin view of your page. Selecting a date will reveal any blocked time slots and the reason they’re unavailable.