When you inherit property that is being rented or leased out, you inherit it subject to all leases. Therefore, you may not terminate the existing lease except 1) if the tenant gives you  good cause (e.g. doesn't pay rent; violates material, or important, lease terms); 2) on 30 days notice if it's a month-to-month tenancy; or 3) as provided for in the lease, if the lease does in fact provide a mechanism for termination. Otherwise, you'll need to wait until the lease term is up--you should not have to renew it at that time.