It depends. If the lease agreement automatically terminates the tenancy at the end of the lease term, and you have not given permission to the tenant to remain, the tenant is a holdover, and you can file an eviction to remove the tenant. If you accept rent from the tenant and have given the tenant permission to remain, the tenancy is month-to-month, and the tenancy will be governed by the terms and conditions of the lease agreement that expired. It is advisable that your lease agreement addresses end-of-lease term processes and holdover situations.