It's not uncommon for this to happen. The initial course of action is obvious, up-vote the new (and better) post. Folks can readily see that it is newer, unless it's buried on a second page of answers. If that happens, then you're probably going to need to look at why the question got so many answers to begin with. It's not always a bad sign, but it's worth examining.
I wouldn't delete existing answers unless they were no longer relevant and offered information that could now be considered misleading or even dangerous. If they're still relevant, just leave them, they represent the time someone put into contributing to the site and it's a shame to discard that unless you're solving a more immediate problem.
Chat is a great facility to use in order to draw attention to new contributions that should by rights rise to the top. Don't down vote the old one just because it now compares unfavorably with the new one, that doesn't make the old answer bad, but simply the new one better.
Over time, this tends to sort itself out pretty well, even on some of our higher traffic sites; don't worry about it too much.