Climate area? Soil and exposure?

Depending on where you are and any regulations you might have to follow, evergreen vines on an ornamental trellis may give the desired privacy sooner than sky pencils.

Also, consider whether an evergreen is needed or whether something with dense, bare twigs or that holds onto the dead leaves might work as well for you.

in addition to Embothrium's questions, how much space is actually available for planting?

7b, more clay than sand, South

big city name..

this MI boy figures anything south of ann arbor MI is.. well.. south ...'

check out link for planting in clay ...

ken

https://sites.google.com/site/tnarboretum/Home/planting-a-tree-or-shrub

yet compact by not taking much space.

==>>>

i not sure you are using compact the way we would ...

if you need to restrict size.. you will need to eventually prune/shear them ...

also.. i highly recommend a diversity of plants .. not a hundred of any one kind ....

ken

Many cannot even consider it but whenever I see the word privacy my first thought is bamboo

So many in zone 7. Don't even consider (Edit: running) bamboo. Nix on Sky Pencil holly.

If part-sun, I'd consider:

Ternstroemia (Cleyera)

Euonymus 'Green Spire'

Camellia sasanqua (select an upright grower)

Many hollies if you can find a smaller variety. Check with your local nursery.

Certain Fargesia make excellent, comparatively small scale hedges in suitable locations. Since this and related genera finally became present on the North American market in a serious way some years ago - after being grown and appreciated in Britain and Northern Europe for a very long time - "bamboo" no longer automatically equates to disturbingly invasive root growth or looming tallness.

Cephalotaxus harringtonia 'fastigiata' would be good for your zone. However they are very slow growing

That grows quite large and broad in time.

houzz has his thing called a ''cover photo''. I put their image of a bamboo privacy screen as my cover photo. Click on me too see if you see if too.

oh, wow. that's a lot of bamboo!

If the site is shady and wet, then how about Illicium parviflorum.

https://plants.ces.ncsu.edu/plants/all/illicium-parviflorum/