The best thing would be to be honest with yourself and the current partner as well as your still existent wife. Figure out if you really want to move forward with the new relationship and then let each of the women know of your plan. It is understandable that your current partner will not feel comfortable when you are still married. She may wonder what is in for her in the long run.
If she is willing to stick around, then it is up to you how to make things happen. One, your current wife is still in the picture and that will be something that any other woman will focus on.