According to the New York State Department of Motor Vehicles, the minimum driving age in New York State is 16. You cannot drive in NYS if you are under the age of 16. If you have a learner's permit or driver's license from another state, you are not exempt from this NY rule.

You must be 16 years of age or older to apply for a learner's permit in NYS. If you are under the age of 18, your parent or legal guardian must sign the consent section of your driver license application. A junior license is issued to drivers under the age of 18 and has restrictions.

So no, at the age of 14 you are not legally allowed to practice or able to learn to drive in the state of New York.