If you do not have that foreign license, then NY State law will require you to have that supervising driver who must be at minimum age 21 and have their own valid driver's license to operate the vehicle that you drive.
Do I need to be a US citizen to get my NY license to drive?
Although citizenship is not a requirement for your license, you must have US Department of Homeland Security DHS documentation that supports your legal status in the country.  The expiration date from your DHS document will be added to your NY State permit, driver license or ID card.