About the only way I can find
to make the TM backup start over again is to erase the disk using Disk Utility.
That will force TM to look at the drive as a new one and offer to back up to it.
Possibly that is not the way you want to go.
With the old library deleted, TM will still want to backup to Restored library as it views it as a new, freshly changed, file(s)
A larger HD would solve this problem and allow you to keep your current backups and move on with a new, full, one with the new drive