Processes in Microsoft 365 for setting up Office apps, redeeming product keys, and activating licenses.
For Office 2016 and later, you can't reuse a product key. You will have to install Office using your associated account. On the new computer, go to https://account.microsoft.com/services and install from there.
You should uninstall from the older computer, if possible.
If activation fails on the new PC, try phone activation. Use the phone number for your region from the article at https://support.microsoft.com/en-us/office/-telephone-activation-is-no-longer-supported-for-your-product-error-when-activating-office-9b016cd2-0811-4cb3-b896-5a6a13177713 (even if you don't see the error message mentioned in the article).