On March 12, 2021, Governor Cuomo signed legislation providing all public and private employees in New York up to four hours of paid leave per vaccine injection to obtain a COVID-19 vaccine.
Is 4 hours enough time? That would depend on when and where you are getting the vaccine which hopefully will expand further,

Section 196-C Labor Law:

“1. Every employee shall be provided a paid leave of absence from his or her employer for a sufficient period of time, not to exceed four hours per vaccine injection, unless such employee shall receive a greater number of hours pursuant to a collectively bargained agreement or as otherwise authorized by the employer, to be vaccinated for COVID-19. 
 2. The entire period of the leave of absence granted pursuant to this section shall be provided at the employee’s regular rate of pay and shall not be charged against any other leave such employee is otherwise entitled to, including sick leave pursuant to section one hundred ninety-six-b of this article, or any leave provided pursuant to a collective bargaining agreement. 
3. The provisions of this section may be waived by a collective bargaining agreement, provided that for such waiver to be valid, it shall explicitly reference this section of law.”
Public employees are covered by Section 159-c to the New York Civil Service Law.