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 Texas sublease agreement is used when a tenant (sublessor) wishes to lease their residence to another person (sublessee). THIS LEASE AGREEMENT (called the "Lease") is between the San Antonio Housing Authority, (called "SAHA" or. A Texas sublease agreement defines the terms that allow a subtenant to move into an alreadyleased rental unit. Form of Sublease Agreement. Sublease Agreement (Drafting Tips for Sublessors). Landlord, at the request of a Tenant or a. Subtenant, shall enter into non-disturbance and attornment agreements with one or more. Landlord desires to lease the Premises to Tenant upon the terms and conditions contained herein.