Hi. Let's remove the word 'new'. Do we need axioms for philosophy? Yes.
To avoid for a claim to be arbitrary, the claim must be backed up by premises, then these premises must be backed up by further premises, and so on, until we reach a starting point, Archimedean point as Descartes would say, or first principle. Examples of first principles of ethics for Thomas Aquinas: do good and avoid evil. Seek truth and reject falsehood.

Do we need an axiom to create a new philosophy? — gunner

No, you don't need new axioms. All you need to do is get rid of the old ones.

And where are you then? Perhaps you need to think through just what an axiom is, what it's for, and what it does. Otherwise, I think Mr. LaCrampe put it pretty well, if not especially exhaustively

And where are you then?

One would be free of the clichés that so many would-be philosophers like to trot out!