It worries me to see this:
Those are dead needles, and on an “evergreen”, one thinks “dying tree”.
But no need to worry after all. Even evergreens lose “expired” needles or leaves. Everything that’s living and growing will eventually discard dead cells, and that’s what’s happening here. The “joint” where the needle or leaf meets the branch develops what’s called the “abscision layer”, where cell activity and enzymes create a weakness, hence leaf- or needle-drop.
You can see that the dead needles are all higher up the branch, while the branch tips are all still green. This is a good thing!
Different species will keep their needles for more or fewer years–the Pinus strobus (White PIne) above only keeps its needles for a year, so there’s constant change happening. I’ll look forward to watching its development.
This Chamaecyparis obtusa ‘Fernspray Gold’ is losing three- or four-year-old foliage. Meanwhile, the green current growth will be turning a wonderful coppery colour pretty soon (hence the name ‘Fernspray Gold‘), before turning green again next late spring.
Your broadleaf evergreens will be doing the same (leaf drop), but may not look so dramatic.
This rhodo is losing three-year-old leaves. You can see that the leaves at the top of the picture are current year’s leaves, then follow the stems down to find last year’s leaves, and finally the third year leaves that are yellowing. But you can see it’s a very healthy specimen–probably the happiest rhodo in the garden.
So as long as the foliage that’s falling isn’t this year’s foliage, you can probably not fret too much about it. If you want to find out how many years your own tree/shrub holds its leaves, U of Nebraska has a page you might find useful. For a little more in-depth reading, inthegarden offers this article.