Does the words brand new have a hyphen?

No, "brand new" does not have a hyphen. It is considered a compound adjective but is not hyphenated when used before a noun.

Here's an example:

* Correct: I bought a brand new car.

* Incorrect: I bought a brand-new car.

However, if "brand new" is used after the noun, it is often hyphenated:

* Correct: The car is brand-new.

* Incorrect: The car is brand new.