Time Machine Backup. How do I change my backups to a new external drive?

If you don't want to lose backups of things that are no longer on your Mac (including older versions of documents still on your Mac), you can move the backup. See information in Transfer Time Machine backups from one backup disk to another - Apple Support

Myself, I just turn off Time Machine and then attach the new disk and turn on Time Machine and select the new disk as the backup destination and let it start fresh.

BrockSF Said:

"Time Machine Backup. How do I change my backups to a new external drive?: So if I have a 2T internal HD my external backup drive should be 6T? Oops I just go a 2T drive. I've only <1T of data at the moment."

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Whole Backups:

Use a an external Hard Drive that Is 3 times the Total Storage Capacity as that of your internal HardDrive, if you want to keep making whole backups.

Uncheck "Back Up Automatically":

If you are not using Automatic Backups, then a smaller hard drive would be fine. So uncheck it, and get an external Hard Drive that is 1.5 the size. Perform this in Time Machine Preferences (Found in System Preferences):

Screenshot of what to Uncheck:

BrockSF Said:

"Time Machine Backup. How do I change my backups to a new external drive?: Will the new backup start where the old one left off. If so, how do i keep them related? Or is it as simple as just backing my whole HD with the new back up drive? Would that contain everything that my old HD has?"

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Using a New Hard Drive for TMB:

No. What is on your old Hard Drive, is on your old Hard Drive. Hence, they will not be related - they will not start where the old one left off.

New Hard Drive:

Use a an external Hard Drive that Is 3 times the Total Storage Capacity as that of your internal Hard Drive, if you want to keep making whole backups. Use Disk Utilities to format the Hard Drive. In it, you'd completely erase it, format it as APFS. and then use the Hard Drive for Time Machine Backups, from then on out. Store it in a safe location that only you are aware of, and only you have access to.