T-Mobile iPhone trade in
I want to trade in my brand new T-Mobile iPhone into apple store credit to buy a phone over seas
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If its a current model Apple is selling (13, 13 mini, 13 Pro, 13 Pro Max, SE 3), Apple will not take it in for trade in. Link-> Apple Trade In - Apple
Also, note Apple will not give you cash for a trade in anyway. They will give you a gift card with the value of the device you can use to purchase another one, but the gift card will only be valid in the country where you made the trade in.
Unless you bought the iPhone from T-Mobile under subsidy, it should be unlocked and can be used overseas just fine.