If you signed a stipulation that did not include a final judgment, you will have to go back to the judge to request the judgment and the warrant of eviction. You will need to file an order to show cause to reopen the case.
If the stipulation does include the judgment or you got a judgment after trial, you can hire a marshal to perform the eviction. The marshal will request the warrant of eviction. Only a city marshal can evict someone from an apartment in NYC.
You can find a list of marshals on the Department of Investigation’s website.
The court attorney in the Help Center can give you more information about marshals.
The tenant may file an order to show cause to ask for more time or to tell the court that you did not make repairs. If the judge signs the OSC, the tenant will serve the OSC on you and you must go back to court on the date scheduled. If you do not attend this court date, the tenant may be able to delay the eviction and you may have to get a new judgment and warrant.