A lease that provides for a specific ending date terminates on that given date. Neither party has to give a Notice to Vacate when the term ends at a certain time by agreement. If the tenant does not move out by the end of the stated term (known as "holding over") and the landlord accepts rent, then the tenant may stay subject to the provisions in the original lease. The tenancy becomes a periodic tenancy for the same period as the original term.
For example, if the lease was for one year, and the tenant holds over with the consent of the landlord, the tenant gets a tenancy for another year, unless the lease provides otherwise. Some leases provide that if the tenant holds over with the consent of the landlord, the tenancy becomes month-to-month rather than a renewal for the full term of the original lease.