Legal Question in Real Estate Law in New York

Provided the apartment is neither rent controlled nor rent stabilized, ou can offer him a new tenancy at an increased rental. If he declines, you may ask him to move. If he does not move, you can go to Housing Court to evict him.

Not having read the original lease and presuming it contained no language regarding renewal at termination or hold-over tenancy, the original lease was converted from a term rental to a month-to-month lease. As Arnold states, you could give 30-days notice to sign a new lease on new terms or, if the tenant refuses, go to housing Court.