If you want to delete an individual client, you can do so either from the Full Client List or from the Client Profile screen. What you'll want to do first is search and find the client that you want to delete the profile for on your Client List. You'll see that there is a button for "Delete Client" next to their name which you could use to delete the client from this view:
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This will bring up the confirmation window to delete the client. If you are sure you want to delete teh the client profile, press the red "Confirm & Delete" button:
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