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.THIS AGREEMENT (hereinafter referred to as the "Texas Lease Agreement") is made and entered into this ____ day of. To do this, the landlord must first agree to participate in the Housing Choice Voucher (HCV) program. Responsibilities: The sublessee is responsible for paying rent to the original tenant (sublessor) as stipulated in the sublease agreement. Your rental housing provider is required to give you a copy of the lease if you request it from them. • Property owners must comply with the City's Property. Applicants must submit one (1) original and two (2) copies of the Residential Lease Agreement with the Moving packet. Unless the lease says you can, a tenant may not sublet (rent the rental property to another person) unless their landlord says it's OK. A Texas sublease agreement allows the original tenant to rent out all or part of a property to a new tenant or subtenant.