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 a legal document that allows a tenant to sublet a property to someone else (subtenant). Also known as subletting. A sublease agreement is a form that allows a tenant to rent space they have under a written contract with a landlord to someone else. Create your free Texas residential sublease agreement. Download our template and learn how to sublet an apartment in Texas legally. State the rent schedule and amount. State the agreed upon rental amount and when the subtenant must pay it. The process is fast and easy.