looks like a hebe, maybe the frost got to it, can cut it back and it will soon grow back again, are the leaves quite tough and shiny? hard to tell by this pic but looks like a hebe to me

It is a Hebe. I suspect that the part that has died has stem damage at the base, often caused by the branch splitting at the base which several types are rather prone to. With Hebe's, it's usually 50/50 if they grow back well or at all after hard pruning which is about the only course of action you caould take here. If it does fail, look at this as an opportunity to re-plant!