If you've already activated Office but are still getting prompted to activate when you open an Office program, install the latest update to resolve the issue.
How to get the update
If you can open an Office program like Word, click Help > Check for Updates and click the Check for Updates button.
If you can't open an Office program, go to microsoft.com/mac/downloads, scroll to the to the Office for Mac updates section, and choose the latest update available. After the screen refreshes scroll down and click the Download Now button.