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.A sublease agreement is a legal document that allows a tenant to sublet a property to someone else (subtenant). Also known as subletting. A Texas sublease agreement defines the terms that allow a subtenant to move into an alreadyleased rental unit. This form is intended for use when a tenant wishes to sublease his or her leased property to a third party. The landlord's consent is required. A Texas lease agreement is a written contract explaining the inner workings of a rental transaction involving a piece of real estate. A sublease agreement is a legal document that permits a tenant to rent out their property to another person, known as a subtenant. Edit, sign, and share texas sublease contract online.