I see two possibilities:
1. There's an Enterprise. Pretty plain and simple, cut-and-dried, and not much story to it.
2. The name was retired after The Burn. I'm assuming there was an Enterprise during The Burn and it blew up along with all the other active ships. The Enterprise represents the zenith of Starfleet. There's no zenith in the 32nd Century. So when Starfleet is fully restored, we'll see a new Enterprise. Whether it's in DSC or another series.
I think the second of these possibilities is more interesting, and better in keeping with the history of the Enterprise's lineage.
The Enterprise is a trophy ship. It's never around when Times Are Tough for a prolonged period. It was kept out of the Klingon War in DSC. On DS9, while the Dominion War was raging on, it was off on wacky Insurrection type of adventures. So it wouldn't surprise me that a Starfleet that's cocooned itself, like in DSC S3, wouldn't have an Enterprise "boldly go where no one has gone before." They're keeping a low profile.