My garden has been on the backburner for a couple of years and my rosemary is woody and lacking leaves. I'm theoretically growing it to eat, rather than look at, so how best do I encourage soft growth?
I would add some fertilizer. Not much, rosemary is a plant of poor and dry soils. On the other hand, if it is a lot woody, probably it has eat most of nutrient in the soil.
I would also check if there are some plants nearby which compete with rosemary. Rosemary is slow to grow (I think also on the roots), and it hates shadow. Really!
Pruning: I would never touch the wood (large branches), but when it is dead. It seems that rosemary doesn't like it. The green parts will cover the wood again. You should prune just the green branches (they are also woody, but round and young).
The good news: from my experiences, rosemary are very resilient. They will growth stronger that before, very quickly. [I assume you have no problem with climate, because the rosemary seems already old].