If you know the URL to your App catalog or are using a site collection app catalog, you can skip to step 5.

1. Open the app launcher and click on Admin;

   

2. Open your SharePoint Admin Center;

   

3. On the left panel, click on More features and select Apps;

   

4. Proceed by clicking on App Catalog;

5. On the left pane, click on Apps for SharePoint;

   

6. Select the older package of the Web Part deployed, click at the option Files, in ribbon, and click to Delete Document;

   

7. Now click on Upload and select the .sppkg file that's inside the spfx folder in your web part package;

   

8. Finally, on the pop up that appears, tick the checkbox Make this solution available to all sites in the organization and click Deploy.

   

And that's it! The web part is now updated for the latest version.