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.You are entitled to request permission to sublet from the owner, and the owner may not unreasonably refuse such permission. The procedure for subleasing is quite complicated. A sublease, or a sublease agreement, is when a landlord and tenant agree to rent out the unit to another resident not originally on the lease agreement. The sublease agreement will reference the master lease agreement between the existing tenant and the landlord. These laws may permit you to sublease even if your lease forbids it. A sublease agreement is a legal document used when a property is leased to a third party.