I don't know for sure, but from browsing the internet, I have found theories as follows:
With lower oestrogen levels, your adrenalin and cortisol (stress hormone) rise in an attempt to get your oestrogen levels up. This probably results in muscle tension. Hence the jaw clenching.
I know that I tend to hold tension in my upper back and shoulders, so practice releasing this at regular intervals which seems to help with the jaw. As I tense, my neck goes down and my shoulders go up and all the muscles round my neck and jaw and face tighten. It also affects chest and so breathing gets shallower which increases the tension.
Yoga, pilates and a good contemporary dance classes help as you become more body aware and learn how to stretch out and lengthen and release muscles which helps. Doesn't always help when you do it in your sleep though.
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Unfortunately, HRT has not helped it for me. I expect it goes away as your body adjusts, although I do remember my Grandma complaining in her 80s.