Dear Hila, Thank you for sharing. It looks to me like your herb plant need a little wrest from watering. The stems look watery, which means too much water.
If you look closely at the soil around your herb plant, you will notice its dark watery color. So before pruning, stop watering for few days (3-4 days) and keep it out of the rain, if it's living outdoors. Let it dry and recover first.
As for pruning, avoid hard pruning so your plant can recover. To nurse your plant back to health, at that stage prune only its top 2/3 (see red marks on picture). You can even pinch it. Also, I strongly recommend moving your plant into a larger container or even planting it in the ground (if you can). Having a larger container will allow more space for the roots to develop, thereby helping in its recovery.
In short - dry your plant, prune gently, replant in a bigger pot or plot, and you will soon have a fine healthy and strong herb.
shrub removal - Of course having a gardener do it is easier, but getting down and dirty is more fun and will give you loads of satisfaction. You can DIY the removal of old shrubs!