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 considered a written document that offers the lessee a chance to pass on the responsibility and rights of tenancy to another person. A Texas sublease agreement allows the original tenant to rent out all or part of a property to a new tenant or subtenant. This section defines a "lease" as either a verbal or a written agreement between a landlord and tenant. A commercial sublease is an agreement to lease space from a tenant rather than directly from a property owner. You don't have to write up a sublease contract. This law is in Section 91.005 of Texas Property Code. Some leases may allow it under certain conditions. In the case of lease assignment, the idea is to transfer complete ownership of the lease from the original tenant to a third party.