NYS restricts driving privileges if you are under the age of 18 and have an out-of-state driver license, or you are any age and you have an out-of-state learner permit. If you are able to keep your MD provisional license the NYS DMV says that you must obey the restrictions of both your home state and the NYS restrictions for learner permits or junior licenses in New York State.
Make sure that your out-of-state provisional license is valid outside the state that issued the permit, Maryland. If it is valid only in the issuing state, you cannot use the graduated license to drive in NYS.
Now you said you are living in New York. If you are going to stay in NYS and be considered a resident, then the New York DMV states that you must get a NYS driver license within 30 days and surrender your out-of-state driver license. This likely also holds true if you have a learner's permit, provisional license or other type of graduated license from out of state. You cannot just exchange an out-of-state permit for a NYS permit, the DMV states you must apply for a NYS learner permit and driver license.
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[Let CarInsurance.com help you find affordable auto insurance now.] So to answer if you can drive with your MD provisional license in New York, yes you likely can as long as Maryland allows for it and you follow the restrictions of both Maryland and New York for your type of graduated license. But if you are a resident of NY now, you will need to check with the New York State DMV to find out what you need to do to apply for a type of New York graduated or full license.
Comment Update: The answer is yes, but you need to verify that you are not a resident of NYS. If you are, then you need to comply with NYS laws and get licensed and registered in New York. | 
