You can always be real and tell your P if you want to explore new working environment. Be sincere. Anw, there isn’t an obligation for you to inform your P but for courtesy purpose, just let your P know. Don’t let whatever she says hold you back if you really want to try for open posting. No one (but only yourself) can stop you from applying for open posting. If your records all the while is good, your P will not be able to stop your application.