A contract in which a lessee transfers his or her rights under a lease to a third party for part of the lease term is known as: a sublease contract.
A sublease contract is a contract that is usually written between the tenant, the subtenant with the landlord's consent.
This contract takes place when a tenant needs to temporarily relocate during his/her lease time. The tenant finds a third party, known as a subtenant, that agrees to take over the payments during the period that the main tenant is not available or is away.