Yellow tangs are very dominate oriented fish. Could take a few days for things to calm down, could never be peaceful. In such small acreage it could be disastrous. Only time will tell. Many people suggest to add yellow tangs last for this reason.
Your coral beauty is a beautiful one, just be sure to supply the tank with dried seaweed, or nori, to help the tang and the coral beauty with added greens. I have a coral beauty in my tank, which is a full reef.....lots of coral, and he has been a model citizen.
Funny though, my coral beauty is the one that always chases any new additions, it's definitely the bully of the tank.
You say it is shy, mine is really shy and rarely comes out in the front of the tank, it stays mostly in the rock work, but comes out....just not as focal as the yellow tang.