A sublease is an agreement where someone takes over part or all of an existing lease. This type of lease involves at least three parties.Responsibilities: The sublessee is responsible for paying rent to the original tenant (sublessor) as stipulated in the sublease agreement. THIS AGREEMENT (hereinafter referred to as the "Texas Lease Agreement") is made and entered into this ____ day of. Subleasing If you do not want your tenants to sublet the property, make sure to include a provision clearly stating this. Step 1: Written Notice to Vacate. Unless the lease agreement says otherwise, the landlord must give the tenant at least 3 days to move out. Landlord, at the request of a Tenant or a. Subtenant, shall enter into non-disturbance and attornment agreements with one or more. Applicants must submit one (1) original and two (2) copies of the Residential Lease Agreement with the Moving packet.