Your DD-214 has to be submitted with an application:
http://www.nyc.gov/html/nypd/downloads/pdf/permits/HandGunLicenseApplicationFormsComplete.pdf
I understand your question to be "Will NYPD issue a license based on my DD-214?" The answer is no they look at a lot more information than that. See also
https://licensing.nypdonline.org/new-app-instruction/
A "Carry" permit is exceedingly difficult to obtain. You should do a web search for different information on this; see for example
NY Gun Forum and (excerpt below)
New York City and Its Gun Laws: How Strict Are They? | Guns of New York
What if I want to use a gun for different situations? Does one permit cover it all?
Not really. There are five kinds of permits in New York City and each allow you to use your gun in specific ways:
* A “premise” license lets gun owners use their weapon only on the premises of the address provided on the license. According to the city’s license division, most New York City applicants apply for this license.
* A “carry business” license allows gun owners to use a concealed gun for employment reasons and allows them to carry it from home to workplace.
* A “limited carry” business license restricts gun owners to use the weapon only of the business address on your license.
* A “special carry” license will let owners use a gun for business purposes and take it anywhere as long as the license is valid.
* A “carry guard” license is reserved for security guards and people in similar jobs. This license needs documentation from the employer.
Is it easy to get a permit in the city?
The National Rifle Association-Institute of Legislative Action says it is incredibly hard to get a gun permit in the city compared to other places. Moreover, the license to carry a concealed gun is the hardest to get. It is given on a “may issue” basis, which means you can be denied the privilege of carrying the gun around even if you own one. This is different from many other states and cities in the country, which do not require you to have a license to carry a concealed gun. Neither New York City or New York state allows a gun to be openly carried.