A sublet, or sublease agreement, adds someone new to an existing lease. Usually the new person (subletter) replaces someone who is moving out.The landlord chooses whether or not to allow this type of agreement. A sublease agreement is a legal document allowing existing tenants to rent out their rented space to another party, the subtenant. WHEREAS, Landlord's consent to such assignment is required pursuant to the terms of the Lease, and the Landlord has agreed to consent to such assignment;. Learn about your rights when it comes to sublease laws in NYC. Tenant must not assign this Lease or sublet all or part of the apartment or permit any other person to use the Apartment. Means a space of ground in a cemetery that is used or intended to be used for an in-ground burial. All capitalized terms herein shall have the same meaning as in the foregoing Agreement. 5. The Guide explains what you should know when applying to rent, living in a rented property, and dealing with the end of a lease.