I do believe it gets better with age but I think you have to work at it. I don't believe it just happens on it's on, because I'm 62 and still have some anxiety. It's not as bad as it used to be but it's still there. I have spent years learning to use deep breathing to overcome anxiety attacks, but I use medication, too, at times that the breathing is not enough.

I came across this article on PsychCentral. You may have already read it.
9 Ways to Reduce Anxiety Right Here, Right Now