I too had this problem. I was told simply to get rid of one or the other - was told this by everyone I could find to ask - many with major dog experience.We had had the new pup for several days when we decided to try what I describe.
Here's what worked for me - I took the new pup to the vet and kept her there over the weekend. then husband picked her up and we met away from the house. Buster (older pup was here first and this is his house to protect (as he sees it). Anyway we re-introduced them on a neutral ground where they could sniff and get to know each other there where no one was top dog. We still had a few aggressive incidents. I got a shock collar for Buster and when he would be aggressive he's get one shock and be sent to jail - a separate cage/pen - 10 minutes first occurrence, increased by 5 minutes each time. After about 3 times, we did away with the collar and I say Buster in my stern voice and he trots off to jail.
They are major loves now. Don't give up - What I think helped too was when I realized when Buster would snap - it was when he felt RedGirlbird (new pup) was trying to be the main protector. Buster sees it as his job to protect the home, his Dogma and his RedGirlBird.
Good luck! You can solve the problem ;)