How do I clear out my passport to add new backup?

If you're referring to a drive, you open it in Finder and delete user data. Or you can erase it completely via Disk Utility. Just remember, once gone, the data is gone.

It may be better to buy a much larger external drive for additional data storage.

If it's your Time Machine drive and it's full erasing and starting from scratch may be the answer. But, TM is supposed to never fill as it deletes older data to continue to operate.

For more specific suggestions, you need to provide greater detail ... drive's size, what it's used for, is it faulting and so forth.

"ideal" size for a Time machine backup drive is 2.5 times the size of what needs to be saved, or larger. a smaller drive can be used, and it will consolidate and eliminate oldest backups over time, so it should never be "full" unless it is way too small.

Time machine works in the background at low priority, so that it does not interfere with your important work. Because of that, do not pay extra for a drive that is fast.

I would NEVER use a thumb drive to backup anything. They are finicky and pure trouble in my opinion for non camera usage.

Get a real drive. Either a Hard Disk Drive (HDD) with a spinning platter (cheaper by slower) or a Solid State Drive (SSD) (more expensive but much faster) and move on past the thumb drive idea. But that's your call.

What brand you choose is up to you; we all have our favorites. I favor Samsung SSDs but have no favorite HDD brand

"Either a Hard Disk Drive (HDD) with a spinning platter (cheaper by slower) or a Solid State Drive (SSD)"

HDD is electromechanical with a spinning magnetic disk. SSD is pure electronics ... no moving parts.

My Passport is Western Digital’s brand name for its bus powered external hard drives. Not my preference since they’re mostly proprietary to USB, but I got one with that branding in 2006.

https://www.westerndigital.com/products/portable-drives/wd-my-passport-usb-3-0-hdd#WDBYVG0010BBK-WESN