Will my sprint Apple Watch connect to my T-Mobile phone?

How is your Apple watch "Sprint"?

The Apple watch cannot be activated on a cellular network independent of the paired of iPhone. The watch and the iPhone must be using the same carrier and the same service plan.

If the Contract with Sprint was cancelled for the iPhone it was paired to, then the watch is no longer tied to Sprint either.

Apple watches are not locked to particular carrier, though as mentioned, Verizon seems to have issues activating watches that were activated on another carrier previously.

If your watch is a cellular model, and you want to keep using cellular service on it, it must be activated with T-Mobile.

If you watch is a GPS only model, or you don't plan on activating cell service on it, then the carriers are irrelevant.

Either way pairing the watch to the iPhone has no connection to the carrier directly. Only if you plan on activating cell service on the watch.

You should be able to pair the watch to any phone. If you're actually asking about using the cellular service with your TMobile phone, that may be a bit trickier. I know there have been reports that Verizon can't activate any Watch that was previously activated on another carrier and they don't really have an answer as to why. I suggest you call TMobile and see if they can help you get it activated.