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.Unless the lease says you can, a tenant may not sublet (rent the rental property to another person) unless their landlord says it's OK. This law prohibits subleasing during the lease term without the landlord's prior consent. Subleasing occurs when a tenant rents out the property to someone else but remains responsible for the lease terms with the landlord. Subleasing occurs when a tenant rents out the property to someone else but remains responsible for the lease terms with the landlord. A sublet is when a tenant allows another person, not on the original lease, live in the rental property with the intent of covering all or part of the rent. Identify the full names of each party and what their role is in the contract. This Sublease pertains to a specific property at the (Street Address) in the City of (City Address), Texas. A Texas sublease agreement allows the original tenant to rent out all or part of a property to a new tenant or subtenant.