[PaulDavisThe1st]

One answer would be that there was no conquering. That could happen via a few possibilities:

1. pre-Clovis people were so thinly spread that Clovis was able to just fill in the gaps

2. pre-Clovis people had actually essentially become extinct before Clovis arrived. It's not easy to see how that would be the case in a continent(s) of this size, but not actually implausible.

3. as a combination of the two, pre-Clovis culture was completely nomadic, and their constant migration kept them out of the way of Clovis until a point where their population was so diminished as to leave no descendants, even via inter-breeding.