External drive for Time Machine

your old TM drive should remove oldest files to make more room as required automatically.

That's the theory. And it works for the most part if the next backup is a small incremental backup.

But....if the backup drive is full and the next backup is larger than normal.....as might be expected after an update or a significant amount of new data has been added......Time Machine cannot delete enough old files to make room for the new backup. Apple never bothers to mention this small detail of course.

Then, you are stuck since Apple does not recommend that users try to manually delete Time Machine files due to corruption issues.

Start from scratch but your old TM drive should remove oldest files to make more room as required automatically.

I agree that is why I usually just start over or get another drive if TM will to longer backup.