sensor o ring

What speed sensor exactly?

The device that attaches to the hub of the rear wheel. (the 510 originally came with a cumbersome chainstay-mounted device & magnet but after it quit working around 2019, Garmin sent me the hub version.) 

seems my previous answer didn't post. here's the short version: it's a speed sensor that is attached to the rear wheel hub.

If it is the Garmin brand one with the silicone casing and integrated attachment string...

There is no replacement casing and attachment string available.

You have asked Garmin support  for a replacement already? Then there is no hope.

You're right. No hope. Called an actual support human after getting nowhere with on-line support. There's no replacement for the necessary insert. They did, however, confirm that an entirely new speed sensor will work with my ancient (but still good) computer. The Garmin website omits the Edge 510 from a list of units compatible with the speed sensor 010-12843-30 but it apparently is compatible. I'll buy it. Thanks for your help in sorting this out!

I find my 510 will work with just about any speed sensor, including the new Garmin ones but also others like those from Magene, which I'm using on one bike.