I would cut it back. The redening at the end looks like it's starting to die back on it's own so I would doubt that one would flower again and it just detracts from the appearance.
Cut it back to the base near where it comes out from the base of the leaves. Cut as close as you can to the plant without damaging the leaves.
Usually I would say that the plant will produce a new spike when it's ready and doesn't need any of the old one left behind for that... but you've already got your new spike so I won't bother