Answer: There seems to be a sort of misperception that Thuja can handle shade. It actually needs full sun to stay healthy and thick. In too much shade it will grow thin and sparse within a few years, and may actually grow taller than normal in its search for light. So you would want to plant it where there is a minimum of six hours of direct sun including the hour of noon -- this would actually be a full sun location. This is true for the vast majority of evergreens.
There are several taller, narrow or columnar arborvitaes (Thuja)that are very popular as evergreen screens or hedges. But that is an unusual size and shape among evergreens, and unfortunately I can't think of anything that would do the same in a shadier site. At one time hemlocks were used for this as they can be pruned, but I would not recommend hemlocks due to the insect problem with wooly adelgids.
You might be able to grow a japanese holly (Ilex crenata, it does not look like a typical holly and the cultivar Sky Pencil only grows to about 8 feet tall) or a boxwood such as Buxus sempervirens (the species reaches 15 to 20 feet tall and wide), depending how shady your site really is. These would be mature sizes if left unpruned -- although they are not terribly fast growing. They will both need protection from winter winds, as well. You might also consider one of the smaller of the Cryptomeria if you have light shade and if your space is wide enough.
I might mention your zip code places you in Manhattan with a winter hardiness zone of 6B, meaning the warmer part of zone 6. If you are really in zone 5 then the holly would not work for you. I would suggest you work with your professionally trained nursery staff for additional suggestions based on a more detailed understanding of the planting site and your design goals. Good luck with your project!
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