A sublet, or sublease agreement, adds someone new to an existing lease. Usually the new person (subletter) replaces someone who is moving out.Shall mean and include any building or structure or trailer or land used as a trailer park, rented or offered for rent to one or more tenants or family units. The landlord chooses whether or not to allow this type of agreement. A tenant who sublets an apartment to another person is the prime tenant. The person to whom the apartment is sublet is the subtenant. Subletting is when thirdparty rents or "subleases" the property from the original tenant. Overview of Truth in Renting Act. 1. Lack of a key could result in the loss of life or property in the case of an emergency. A sublet is when a tenant allows another person, not on the original lease, live in the rental property with the intent of covering all or part of the rent.