How long till the new one can run on its own? If you don't put any media from a working filter inside it, I am not sure. probably into several weeks.
Also putting the new filter on an already established tank still requires the old one? Tanks are mostly "established" by the filtration system which does the waste conversion work. There is some beneficial bacteria on other surfaces, but you need a sufficient beneficial bacteria-to waste-ratio in order to prevent toxic levels of ammonia & nitrite.