G'day Linda, I'd say it'll be alright. the youngest parts show the effect of frost bite first, then older parts start to give up. But if you prune off the dead stuff when it appears and perhaps feed it some sulphate of potash it should be okay. From the photo it looks healthy where it isn't dead :-) Go well

Do you have it growing in a good, coarse potting medium.....one that drains freely? And does it need to be repotted?

And have you been fertilizing it once in a while with a properly balanced fertilizer? Plants require a lot more than just potassium, especially when growing in containers.

Thanks for the feedback everyone. I do have the plant in a well draining potting medium. Never thought about repotting it so soon. I just repotted it last year. Do you think it needs a bigger pot?

I have only been fertilizing with fish emulsion every once in a while. Should I get a better form of fertilizer?

It is probably root bound.
Needs to be taken out, its roots trimmed off and repotted in a new well drained potting mix, with well balanced pH. Herbs prefer alkaline soil ( pH =>> 7)

I give mine a half table spoon of Epsom salts in two cups of water when they look alil sad. ... when u repot put a few small river stones in the bottom improved drainage a lot