I just updated from Mojave to Catalina and now my external hard drive is inaccessible.

That driver might need updating to work with Catalina.

Other trouble shooting steps you can take include SMC Reset, and booting into safe mode. But I suspect that it is this third party NTFS driver that needs an update to work with Catalina.

If you can update the driver, you can continue to use NTFS. If you need to mount the drive on both PCs and Macs, you might need to keep NTFS.

However, if it is option for you, it might be best to reformat the drive to HFS+ or APFS so as to not encounter this dependence on third party software during future OS updates/upgrades. You first need to copy your files off from the drive to save them before reformatting. Since it is NTFS, it should mount on a PC (Windows). You will need to temporarily place the files somewhere you can access from a Mac, maybe cloud storage. You can in principle continue using NTFS but you would need to pay attention to keeping the NTFS driver current.

There is always a possibility that the drive has failed. That can also be checked first on a PC, before proceeding.

So, if it's simply a case of me moving all the stuff I have on the Toshiba (not all that very much, thankfully) to a temporary drive, reformatting the Toshiba to a Mac-friendly format, and finally putting all the data back to the Toshiba, then I guess that's what I'll do.

That's what I'd do. Format it as shown in this screenshot:

Do you know how it was formatted?

Most consumer drives come formatted for Windows and tell you to install software to use the drive.

That software often fails after an update, and will sometimes prevent the drive from mounting.

You cannot reformat the drive without losing the data. Move the files off the drive and format it for use on a Mac. Then move them back.

You will have no end of trouble trying to maintain the software required to keep writing to NTFS.

Fartgum wrote:

...Only thing is that now apparently I'll have to pay for it once the trial period ends, whereas the version I had been using before was free because it came with.

This bothers me, that you are being charged for these drivers. I guess I've grudgingly finally made peace with ongoing fees for Office-365, and some Adobe software, but this is simply a driver so you can mount the disk. Is there a separate fee for every single disk??? And, as Barney points out, this will likely be a recurring problem with any or each update from Apple to the OS, sometimes even security updates have resulted in incompatibilities with these special drivers. After every new update, scores of people post " ...now I can't access my external drive" because of these things. Unless you have a requirement to be able to read the drive on a Windows machine, I would reformat it (after safely copying the files off) to a standard format (HFS+ or APFS) and then you won't have to worry about these surprises.

The major system upgrades removes the NTFS software needed to access the drive. You'll need to reinstall it, using the latest version from the developer.