No, being a current tenant gives you no right to automatically renew a lease, anymore than being someone's current plumber means that person cannot stop using you and pick a different plumber instead. A landlord is free to decide who to lease to--current or former tenant--just as tenant is free to decide whether he/she wants to renew a lease or not. If the lease has an automatic renewal term in it, or some other provision giving you renewal rights, that would be different: a contractual obligation to renew is enforceable. But if the lease doesn't require renewal, the landlord is free to select a different tenant.