A sublease agreement is a rental contract used for rerenting a currently leased unit to a new tenant. A sublease agreement is a form that allows a tenant to rent space they have under a written contract with a landlord to someone else.A Sublease Agreement is a contract that outlines the terms of a sublease between an existing tenant and a subtenant. A Texas sublease agreement defines the terms that allow a subtenant to move into an alreadyleased rental unit. The terms and conditions of a sublease agreement should be very close to those in the original lease signed with the landlord. How to write a sublease contract Provide a description of the property. Add the names of the tenant and subtenant. As stated above, the Landlord for this property is . In fact, a tenant must get permission from the landlord before they sublet as per Section 91.005 in the Texas Property Code. Sublease is a legally binding contract made between a tenant and a new tenant (also known as a subtenant or a sublessee).