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.Landlord owns certain real property and improvements located at. (hereinafter referred to as the "Property"). Responsibilities: The sublessee is responsible for paying rent to the original tenant (sublessor) as stipulated in the sublease agreement. A Texas sublease agreement is used when a tenant (sublessor) wishes to lease their residence to another person (sublessee). Funding Agreement entered into between Subtenant and Tenant. Tenant's Insurance Coverage. Tenant will provide such self-insurance as it deems advisable to insure against loss of any of its property in the Premises. A sublet, or sublease agreement, adds someone new to an existing lease.