I have a 6 foot white vinyl fence around the sides of my yard, however my neighbor can still see into my pool from their windows on both stories. So I would like a natural fence that would go even higher. The area gets decent sun however there are other trees nearby so I would call it partial shade.

I am looking for help as a total newbie to gardening, on what to plant near the fence.
I was going to plant Leyland Cypress but it seems that the largest growth is on the bottom as it's a pyramid shape. I already have coverage on the bottom and I only need privacy above 6 ft. I don't care if it's an evergreen or not as the only time it makes a difference is summer. Something that grows relatively fast with dense coverage would be ideal. I have approx. 15 feet of width that I need to cover.
Thank you for your help.