Subleasing: In subleasing, the original tenant transfers the entire lease agreement to a sublessee for the remaining duration of the lease term. 2. A tenant who sublets an apartment to another person is the prime tenant.The person to whom the apartment is sublet is the subtenant. You can lease your apartment to another person. If you will be returning to live in your apartment after the other person leaves, this is called a sublease. Subletting is when thirdparty rents or "subleases" the property from the original tenant. Subleasing is an agreement where an original tenant leases a rental property to a new subtenant for a set period of time. We open our leasing cycle on November 1st for the upcoming year. A sublet, or sublease agreement, adds someone new to an existing lease. Usually the new person (subletter) replaces someone who is moving out.