Its your choice. If you use rosemary, cut some back. Especially any branches that have few leaves at their bases. These, you can cut back to a couple of inches from the soil. Usually they will sprout new branches, but if that stem is old, it may just not grow. Because they have flowers, it seems to be quite healthy. A little nitrogen based fertilizer will also help. Be sure its not a chemical based one, like Miracle Grow! Using that, will make the rosemary taste very odd.

Sorry to hear of your loss.

Thank you ksrogers. On both accounts.

So, if I cut back, I shouldn't take more than 1/3 of the plants growth, right?

Yes. If some of the stems are long and have no foliage near the soil and upe several inches, they could be cut shorter. Some forms of rosebary have stiff enough stems that they can be used as skewers for a shishkabob.

Cut it back a little way if you like, but it seems to be doing quite nicely on its own. Personally, I'd leave it for a little longer, since it has moved house on top of everything else.

Sorry for your loss.
You've received good and varied advice above, so prune or leave as you wish. Its a good time of year to start rosemary cuttings.

Thank you granite and daisy. Much appreciated.

I will try and send a photo of the above-mentioned rosemary plant, so you can get a better idea of how it looks.

I use rosemary a lot.

I am with holding my comments until I see some photos.

Here in Z6, that would all be dead. Well trimmed shrubs.