If you are upgrading the bike I assume (maybe incorrectly) that you are going to disc brakes also?? If not, I would strongly urge you to think about a new bike with disc brakes. The 10 speed Zipp certainly is not disc brake compatible. FYI - I just went through the same thing with a new bike and Sram AXS. I just felt it was time ti start converting my whole ecosystem. So, I ended up getting new Zipp disc brake wheels. The only problem is that I like the AXS, 12 speed, disc brakes so much that I now want to upgrade my road bike. And so it continues . . .

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David
* Ironman for Life! (Blog) * IM Everyday Hero Video * Daggett Shuler Law *
Disclaimer: I have personal and professional relationships with many athletes, vendors, and organizations in the triathlon world.

I am assuming we are talking TT bike the brakes are irrelevant so its possible but will be more cost and hassle than what its worth.

For the 12 seed AXS you need an XDR driver and for your bike that can accept QR endcaps with standard road spacing. This is a bit of an odd combination given most people will by using the wider 12x142 spacing with the XDr driver. I don't think anyone such an adaptor that fits onto your hub but even if they did I believe you would need to re-dish the wheel. A rear Zipp 606 is just a rebadged 808 so it wouldn't be hard to save the rim and rebuild it with the required hub but it will be expensive.

"assuming we are talking TT bike the brakes are irrelevant "
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I would strongly disagree assuming you also train on the bike (or do courses with curves and hills). I thought the exact same thing as you until I got caught in the rain in mountains on my TT bike . . . the disc brakes are an incredible game changer and safety feature.

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David
* Ironman for Life! (Blog) * IM Everyday Hero Video * Daggett Shuler Law *
Disclaimer: I have personal and professional relationships with many athletes, vendors, and organizations in the triathlon world.

Nearly 100% of people in your situation just wind up selling those old 606's and buying new wheels.

This. They're also useful in actual TTs. In one of my most savagely disappointing losses, I came in 2nd to Thurlow Rogers in a TT. I did a Strava analysis. We were dead even except he braked later going into a sharp turn. That was the entire ~1 second difference between first and second.

I'm pretty sure that 12 speed AXS uses the XDR driver body.

So if you cannot find a new XDR cassette body for your Zipp hub (or whatever hub you have) you would have to replace the hub on the wheel.