Is it possible to reinstall Office 2011 on a newly installed MacOS HighSierra? Do I need to install an older OS?

Well, what MS means is a lot of security issues have been found after the last update for 2011 was released. Regardless, they stopped supporting Office 2011 quite a while ago, and I also just remembered they shut off the activation servers for it. So even if you did install the software, you wouldn't be able to complete the activation process to use it. In short, it's time to throw the software away.

You can install it, though Office 2011 didn't work well for many users in High Sierra.

I would guess it depends on what features you use. Simpler documents? Probably won't notice an issue. Complex? Might not behave as expected.

Of course, make sure to update it to the last version MS made available. Don't recall if 14.7.7 was the last one, but here's a link for it.

https://www.microsoft.com/en-us/download/details.aspx?id=55942

Kurt,

Just before High Sierra was released, Microsoft said in one of their release notes that they did not test Office 2011 for Mac on High Sierra, and then retired the product right after 14.7.7 was released in Sept 2017.

Yup. My note was based solely on reports of users here. Some said 2011 worked well for them in High Sierra. Some said they had problems but was usable. And others said it didn't work at all.

Basically, trying to use Office 2011 in High Sierra was a crap shoot.

Look into the Free LibreOffice, it handles MS Office files like Word & Excel…

https://www.libreoffice.org/