When a tenant does not leave after a Lease Agreement expires or after a Notice of Non-Renewal, they are called a holdover tenant. If you do not plan on renewing a lease, you need to provide ‌ your tenant with a Notice of Non-Renewal within a certain amount of time. The amount of time depends on the location of the property and often how long the tenant has lived in the unit. If the tenant does not vacate before the end of that time, then a landlord can start the eviction process. Depending on your state or local law, before filing in court, you may be required to send an Eviction Notice after a Notice of Non-Renewal does not prompt a tenant to vacate.
In most states, if a tenant does not leave after a lease ends, and the landlord does nothing, the lease will either automatically become a month-to-month lease, or it may renew for the same amount of time as the original Lease Agreement, under the same terms.