Change from one PhD-Program to a much more prestigious (and better paid) new program at my institution
Just talk to your advisor. Since he participates in the program, he will know if you are qualified to apply and stand a chance of getting the position. He will probably also be able to tell you if the two of you will be able to continue working together – after all, it's far from unheard of that a PhD student has a nominal advisor for administrative reasons but a "real" co-advisor who is responsible for the day-to-day research.

In any case, it seems completely unlikely that you would get the position without support from your current advisor. If anything, it's probably that you will need letters of recommendations, and an application without a good letter from your current advisor is an application that is headed for the trashcan.

Just go see him in person – I would avoid email – and start a conversation with "I heard about this new PhD program with much better conditions than the one I have, do you think I could get into it and still continue working with you?". Then see where it takes you. Maybe your advisor knows a reason that would prevent you from applying altogether and you are fretting over nothing. Or on the contrary you are the perfect applicant and you will start earning twice your current salary in a few months. Until you talk with him, you don't know.