Looking for Investor Perspective on Tenant Protection. NY

[Cristian Paez]

My cousin has a new landlord who just recently purchased the 2 Family home. They are paying and current leases are up. The new Landlord is looking to provide new Leases and I believe raise the current Rent. With the coming month getting closer does he have any right to maintain the current rent? I am going to negotiate for him and review the lease but I wanted to ask the bigger pockets community to get their opinion on what can the landlord legally do. It is a Low-Income apartment not paying much but must also take into account that it isn't in good condition. It is a small 2 Bedroom apartment right now going for 1600 per month. The new Landlord purchased the property last month. 

Thank you for your help.