Unlock Apple Watch
How do I unlock the cellular carrier?
Apple Watch Ultra
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Apple Watches are not typically locked to a carrier - Unless they were a subsidized purchase made directly with a carrier.
If you didn't purchase the watch on a subsidized purchase plan with a carrier, you should be able to move the watch to any carrier, which supports Apple Watch. But that carrier MUST also be the same carrier you use for cellular service on your iPhone.
I'd recommend reaching out to your cellular plan provider for your iPhone as the best place to start.