Can I add a hard drive to Time Capsule and back up using Time Machine?

In theory yes, if the hard drive connects to the USB port on the Time Capsule.....and.....the hard drive has been formatted in Mac OS Extended (Journaled). Time Machine will start a new complete backup of the Mac to the hard drive in this type of setup.

However.......the USB port on the Time Capsule is an old and low power design......so.....

• Backups to the hard drive are going to be about twice as slow as backups to the Time Capsule.
• You may need to use a powered USB hub with the hard drive, even if the hard drive has its own power supply

Finally, I would not recommend that you consider doing this type of setup if the Time Capsule is 5-6+ years old, since the Time Capsule's power supply tends to start heading downhill about that time.

The Time Capsule hard drive is no longer usable for back up, but the wireless network is intact.

What model TC are you using?

Is the TC creating the wireless network or do you have another router? If yes, make and model please.

What OS is on the computer/s you are trying to backup? The TC is definitely out of date for latest OS, 11 and 12.. and woeful for windows.

Any recommendation for a wireless router to replace the Time Capsule for my small office wireless

My Asus RT-AC88U just suffered the common 2.4ghz wifi failure issue. It is 5years plus so due replacement. I could continue to use it for router duties and just use a different WAP.. (wireless access point). I have set this up for people who have had similar problems but the Asus still works well as main router.

I reverted to my Synology RT2600AC which is working well. I used it as WAP for couple of years.. IPv6 did not work back then but latest firmware update has now got it working. Not as easy as the Asus to configure but very good and reliable unit.

Buying again I would go for new AX models which should be released soon. First half of 2022 is expectation.

See info here.

https://nascompares.com/2021/12/02/synology-rt6600ax-wifi-6-2-5gbe-router-revealed/

AX is a big improvement so for now just plug the 8TB into the TC (or better directly to the Mac) and use it for backups.

IMHO for network backups, a Synology NAS is much better option cf a router with hard disk hanging off it. Cost wise a cheap end Synology.. 2 bay even second hand recent model will work far better. And is not likely to cost that much more (including 8TB NAS drive) than new AX Synology Router. It is more expensive outlay but routers (new AX Synology??) do not support full SMB3 protocol which Apple now uses by default.. and must fall back to AFP to keep using the old TC.

Synology and Asus offer high performance routers that include a modern USB 3.0 port that support Time Machine backups to a hard drive connected to the router, so this type of setup would far outperform a Time Capsule.

My first choice in this type of setup would be the Synology router, since that company also offers high performance Network Attached Storage (NAS) products with full support for Time Machine.

https://www.synology.com/en-us/products/RT2600ac

In terms of simplicity, the fastest and most reliable solution has always been to connect a hard drive directly to your Mac and back up that way. Great for desktops, but not so convenient for laptops.

I’m working with a mix of Synology NAS boxes and Ubiquiti access points at various sites.

Haven’t worked with the Synology Wi-Fi routers, but their NAS boxes have been solid.