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.Please use the form below to ask any question. We will attempt to answer as quickly as possible. A Texas sublease agreement is used when a tenant (sublessor) wishes to lease their residence to another person (sublessee). Create your free Texas residential sublease agreement. Download our template and learn how to sublet an apartment in Texas legally. The Texas sublease agreement is a useful rental form that can be implemented when the tenant of a property wishes to convey occupancy to a new tenant. A Texas sublease agreement defines the terms that allow a subtenant to move into an alreadyleased rental unit. This form is intended for use when a tenant wishes to sublease his or her leased property to a third party.