Will mathematics journals accept a non-novel theorem, but with different approach Suppose a researcher comes up with a mathematical theorem, which can be obtained trivially from discovered theorems, but with an approach, that was never used before to describe or prove the theorem.

Then do the journals accept the paper because of the new approach or reject the paper because of no novelty?
There is more to mathematics than theorems. Sometimes the best part is the  methodology of the proof, especially if it can be used to also solve important problems in the field. If everybody has been thinking in a certain way about a class of problems for a hundred years and you give them a new way to think about it, you have made an important contribution. 

So yes, a journal would publish that. But your paper needs to be clear about the novelty and importance of your approach. 

My own dissertation had interesting theorems, but was noted for the proof of one of them that was something entirely new and unexpected.