Translation:Do you know who the new principal is?
Do you know who the new principle is? Is already correct! Because you can't make 2 questions in the same sentence. Which means the word "Do you know" already represent the question sentence. That's why you must say "the new principle is" as a positive sentence. This is the grammar.
I disagree! It is a yes/no question (whether you know or not who the new principal is) which is indicated with 吗 at the end! 谁 in this case is not constructing a direct question, it's indicating an unknown person! The sentence is correct as it is: 你知道新教长是谁吗？ or it could also be: 你知不知道新教长是谁？