What word means "to make something obsolete"?

I don't know if this is exactly what you're looking for, but the verb supersede is close.

From Cambridge Dictionary:

supersede — to replace something older, less effective, or less important or official:
Wireless broadband could supersede satellite radio one day.

From Merriam-Webster

1a : to cause to be set aside
1b : to force out of use as inferior.

to supplant TFD

1. To take the place of; to replace

As in:

"The automobile supplanted the horse and buggy."

Obsolete

It's less commonly used as a verb than an adjective (my subjective opinion), but that's exactly what it means.

https://www.merriam-webster.com/dictionary/obsolete

obsolete

 verb

ob·​so·​lete | \ ˌäb-sə-ˈlēt  , ˈäb-sə-ˌlēt\

obsoleted; obsoleting

Definition of obsolete (Entry 2 of 2)

transitive verb

: to make (something) old-fashioned or no longer useful : make obsolete

Interestingly, you automatically used a word in your question that you didn't even comment on—perhaps without realizing what you'd done: displace:

1 a : to remove from the usual or proper place
specifically : to expel or force to flee from home or homeland
// displaced persons
1 b : to remove from an office, status, or job
1 c obsolete : to drive out : BANISH
2 a : to move physically out of position
// a floating object displaces water
2 b : to take the place of (as in a chemical reaction) : SUPPLANT

So, in your example sentence:

The automobile displaced the horse and buggy.