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. The current softness in the commercial property leasing market has created a renewed interest among tenants in protecting themselves against the possibility. Texas law gives the landlord or the tenant the explicit right to end a lease early in a few specific circumstances. A sublet, or sublease agreement, adds someone new to an existing lease. Usually the new person (subletter) replaces someone who is moving out. A complete sublease occurs when the original tenant leases out the entire property to a subtenant. The landlord must also provide smoke detectors.