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.Take over a used car lease. No money down leases! We can help you lease excess space in Houston office buildings, Houston commercial real estate, and Houston commercial property. Get more information regarding the area and surroundings. Get details and reviews regarding a particular Houston accommodation. A Sublease Agreement is a rental contract between an original tenant and a subtenant. We have put together some really amazing deals on New vehicles, and all are calculated with Zero Down. A Texas sublease agreement is used when a tenant (sublessor) wishes to lease their residence to another person (sublessee).