Use Disk Utility to erase and format the old TM hard drive.
see steps 1, 2, 3 and 4 at > http://www.idownloadblog.com/2017/05/24/how-to-erase-format-disk-mac/
Then create some new folders like Pictures, Music, etc on the external drive using Finder, then start copying or dragging and dropping files from your Mac into the Folders on the external drive.