If I have two sticks of 2666mhz dual channeling and buy a pair of 3000mhz will the new pair run slower to match the slower ram?
Yes, if you can get them to work at all. Should be same primary timings for every stick so slowest dictates speed. I have 2 sets of 3000 mhz @ 15-17-17-35 or something, same timings. Still, it took some tinkering to get both kits to work together. One set is Samsung, other is Hynix. 2800 Mhz was quite easy but 3000 Mhz proved to be a problem. Solved it eventually. It helps if you've ever overclocked RAM. If not, you got a lot to learn, if you are into that.
In your case, I would go for 2666 Mhz with the same timings as your old sticks, if possible. But then again, maybe it's time to get a new kit, maybe more capacity and ditch the old sticks. Depends on what you want or need more RAM for. And financials of course.
Whats your motherboard and CPU?