Hi "X", and welcome to Anxiety Zone...
Chewing gum is considered a form of distraction therapy. Now for me, I am open minded to the point of hey, whatever works for you, do it. That being the case, you can try substituting a piece of hard candy, like a Lifesaver, for the gum, if your new job will permit that.
However, one of the main effective treatments for anxiety is cognitive behavioral therapy (CBT). CBT teaches you breathing techniques, and teaches you to face your fears. So in this form of therapy, you don't use any type of distraction, as that is considered a crutch, and you are just masking your anxiety rather then facing it.
I just started CBT several weeks ago, so I am in the early stages of learning this form of therapy. But I can already see the power in how it works, and that it has a sound foundation.
The very best to you, "X", in your new job, and working through your anxiety!... Chuck