Hi, 

These look like Eastern Arborvitae, Thuja occidentalis—maybe 'Emerald Green'. Unfortunately, they are deer candy, so they will not grow back and will keep getting eaten. Unless you were to put an 8-foot-high fence to keep the deer away from them, however, then you wouldn't need the plant for privacy. 

This looks like it is full sun and with it being right next to the road, perhaps an upright juniper species would work better! They tend to be a bit more bristly and deer don't like the sharp texture. Since the planting location is immediately adjacent to the road, a plant that can tolerate salt spray and higher salinity in the soil is a good idea as well. Assuming you don't have a large width to work with, here are some options: 

•  Juniperus scopulorum 'Skyrocket' -native to west coast
• Juniperus virginiana 'Emerald Sentinel' is more of a regional native plant that would work well too. 
• Juniperus chinensis 'Blue Point' - non native not invasive
• Juniperus chinensis 'Gold Cone' - non native not invasive, may not be tall enough at 5 feet max height

Let us know if you have any further questions. 

Emily