As of November 2020, you will need to upgrade macOS to continue receiving Microsoft 365 and Office for Mac updates.
Office for Mac supports the three most recent versions of Apple's macOS. With the release of macOS 10.15 Catalina, Microsoft 365 for Mac and Office 2019 for Mac support macOS 10.15, 10.14, and 10.13
Microsoft 365, Office 2019 for Mac:
As of the November 2020 (build 16.43) update for Microsoft 365 for Mac or Office 2019 for Mac, macOS 10.14 Mojave or later is required to receive updates to Word, Excel, PowerPoint, Outlook and OneNote. If you continue with an older version of macOS, your Office apps will still work, but you'll no longer receive any updates including security updates.
Upgrading your operating system to macOS 10.14 or later will allow Office updates to be delivered for your apps. Note that new installs of Microsoft 365 for Mac or Office 2019 for Mac will also require macOS 10.14 or later.
Microsoft 365, Office 2016 for Mac:
Support for Office 2016 for Mac will end on October 13, 2020. All your Office 2016 apps will continue to function—they won't disappear from your Mac, nor will you lose any data. Learn what Office 2016 for Mac end of support means for you
Word, Excel, PowerPoint, Outlook, and OneNote will install and run on OS X 10.10 Yosemite and later.
For the best experience with 10.15 Catalina, be sure to keep your Office apps up-to-date. If the version of Office installed on your Mac is earlier than 16.16, and you are not being offered updates, you can download the latest Office for Mac suite installer. See What version of Office am I using?.