Is KotOR Ultimate: Taris Upper City free?

Yes. KotOR Ultimate: Taris Upper City is released under Free fan mod (see the download page) and costs nothing. Neither it nor STAR WARS™: Knights of the Old Republic has any paid content.

What do I need to run KotOR Ultimate: Taris Upper City?

STAR WARS™: Knights of the Old Republic, which is itself free. KotOR Ultimate: Taris Upper City is an add-on and will not run standalone.

How do I install KotOR Ultimate: Taris Upper City?

The PlayBound Launcher installs it in one click from STAR WARS™: Knights of the Old Republic's mods list. You can also install it by hand — full steps are on this page.