I too wish you the best, you deserve it and so does this great gal that has so much promise!
Simply, you are moving on with your life, your ex should be of little concern right now. You should do whatever makes you happy. If she snoops, she is taking a risk (just as we do when we let curiosity take over, that is on us).
I do know our ex's can be volitile. Unless you are afraid she will cause trouble by reaching out to your new love interest and meddle there... you really have a lot of control as far as the impact of any of her moves.
She is your ex. You are moving on. Your lives are now seperate. Your only concern right now should be with your life, not what the ex is thinking or feeling. If you find yourself still wallowing around in that, you do have some work to do on detachment.
I hope you are able to pour your attention into getting to know this new person, and feeling safe enough to feel a real connection with her. You will only be available to the new girl if you free yourself from the connection with your EX. Otherwise, you are emotionally unavailable and it isn't entirely fair to this awesome new chickadee... .if you catch my drift

Wishing the best and the least amount of drama possible
