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. A subletter is someone who takes over the lease agreement from the original tenant, known as the sublessor. Therefore, if the landlord wants any changes to the sublease terms, it must spell them out. This Sublease Agreement is available for use on UpCounsel. A Texas sublease agreement is used when a tenant (sublessor) wishes to lease their residence to another person (sublessee). Writing a sublease agreement. Here's a sample letter for when you give notice on your rental. Apartment advertisements AVAILABLE FOR SUEASE NOW!