Sublease Agreement – A rental agreement for an apartment in which a current tenant must rent the apartment to another person. The Tennessee Sublease Agreement is a tenancy form used by a tenant to transfer some or all of their leasable area to another person. This type of agreement must be submitted to the owner or lessor before signing an agreement. The tenant who rents their surface (subtenant) may wish the potential new tenant (subtenant) to complete a rental application form before submitting a sublease agreement. If something happens with the accommodation and. A fixed-term lease simply expires at the end of the rental period.