A Texas sublease agreement is used when a tenant (sublessor) wishes to lease their residence to another person (sublessee). A Texas sublease agreement defines the terms that allow a subtenant to move into an alreadyleased rental unit.Sub-lessee agrees to make monthly rental payments to the Landlord in accordance with the terms of the Lease Agreement between Landlord and Tenant. Bexar County Notice To Vacate Form – Fill Out and Use This PDF. On these items the staff is seeking direction from the. Council or providing information in a written format. 4 6 (d) In the event of a sublease where the rental per square foot established in the sublease exceeds the.