TeamViewer, the erstwhile remote control software that we here at IvanExpert use for remote controlling our clients’ computers, has, like every other company, been hard at work trying to figure out how to get more money from their existing users. So, they have been narrowing the lane in which personal users can use it for free. (Paid users are unaffected.)
Specifically, you will have to be using the current major version of TeamViewer, or it will refuse to connect. This can be a problem if you are running an older version of macOS that doesn’t support the latest version of TeamViewer. This support article lays out it out, refreshingly bluntly: “If your hardware does not allow an update to the latest version, unfortunately, you cannot benefit from the free version.”
In practical terms, this means you’ll need to be running at least macOS 10.14 Mojave on both computers if you are installing TeamViewer from scratch, and want to use it for free. If you already had TeamViewer 15.x installed on an earlier version of macOS, that might continue to work, for the time being.
(macOS 10.13 High Sierra tops out at TeamViewer 15.19, and macOS 10.11 El Capitan and 10.12 Sierra top out at TeamViewer 15.2. The current version as of this writing is 15.21. TeamViewer lets you download the final major versions all the way back to version 8.x, but not these “in-between” versions. So if you’re downloading fresh, you can only get TeamViewer 14.7, which will no longer work for free. This TeamViewer support article details which versions of TeamViewer are compatible with which versions of macOS.)
A viable alternative is AnyDesk, which works on fairly old versions of macOS, as well as current ones, and operates for free without any hassle, in a manner very similar to TeamViewer.