Where is it located and how is it being grown...indoors/outdoors? Container or in ground? If in container, type of soil used?

Looks like spider mites are contributing to the problem, too.

Rosemary is finicky in containers. If you dont have a frost danger, get it outside where it can get lots of light and some natural predators and wind to mitigate the spider mites. Check your drainage and consider reporting into a citrus/cactus type potting mix because rosemary will get root rot in consistently wet, soggy, or compacted medium. Let the soil dry out between waterings. Consider clipping the worst of the dead stuff back and see if you can get new grow th further down and keep the shape from getting too leggy.

I’ll bet if you pulled the plant out of the pot you might
see that it’s root bound. If it is
just cut back all the tangled roots and repot it in a good soilless medium.

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