If you already have a Quake installation that contains a 2.x version of Quakestarter, and you want to replace the 2.x Quakestarter with a newer 3.x version, you can just overwrite the existing files with the new files. You should probably check the Changelog in the new documentation to see what has changed, in case there’s some new thing you want to take advantage of.
Note that the first time you run Quakestarter after a 2.x-to-3.x upgrade, it will remove the old 2.x documentation.
However if your Quake installation contains a 1.x version of Quakestarter, and you want to replace the 1.x Quakestarter with a 2.x or 3.x version, you’ll need to address some things. Please see the 1.x to 2.x upgrade instructions archived on GitHub. (These will also apply to any 1.x-to-3.x upgrades.)