I had one tree and two bushes next to each other. One of the bushes died as a casualty of some underground pipe work, so I removed it. The other two are bare where they had been up against the third. It's been a few years and those bare spots have not grown back. The other sections of both plants seem to be doing well enough. The bare spots are on the shady (north) side. Is there a way to to bring the bare spots back to life?
This looks like Arborvitae and a Tam Juniper. No, there really is not a way to get them to revive at these spots. If you were to prune so that the tops are narrower than the bottoms of these shrubs that would help a bit but these shrubs are quite mature and this looks like their shady side. I'd get a soft, deciduous shrub to fill that space such as a bridal veil spiraea planted at least 3 or 4 feet away from these two shrubs.
What I am worried about is a fairly horrid disease called phytophthora which affects arborvitae an awful lot. The juniper is bare just because of lack of sun. Tell us more about the arborvitae you lost, what did you notice first, how long did it take for complete kill? Phytophthora is still in that soil. Watch the rest of your arborvitae closely. Take pics and send. Or get a soil sample and send to your nearest cooperative extension service (part of a University in your area).