What would you claim? You can claim sales tax on the purchase if you are using the sales tax method to itemize deductions. What else do you feel you might need to claim?
I was thinking out-of-state purchase? How, or do I need to file the car purchase/registration either this year with NY state filing or next year with TX filing?
No, this is not an "out-of-state" purchase that needs to be reported on your tax return. Out-of-state purchases are those for which NY sales tax (or a reciprocal amount) is not paid. Vehicles are different, because when you register the vehicle in NY, you will either pay state sales tax or a balance of sales tax after your Texas sales tax is credited. That question refers to something like a catalog purchase or an online purchase for goods you will use in New York for which sales tax normally is collected but was not. New York wants those items to be reported to collect the appropriate sales tax. But a vehicle is not in this list because that tax will be accounted for.