You can only process the tenant`s personal data in the legal way defined in the RGPD. In the past, you may have simply had a clause in the tenancy agreement in which the tenant signs that they agree that their data should be processed by you. This may now be illegal. Although the RGPD has consent as one of the legal ways to process the data, it is not recommended to rely on this ground in a situation between the landlord and the tenant. This is because there may be an imbalance of power with the landlord who has a position of power over a tenant. Since the tenant can revoke his consent at any time, it would not be in your best interest to rely on consent. Personal data is required because you have a rental agreement or license with the tenant and you must both meet your obligations under this contract. It also involves, where it is necessary, taking action before entering certain steps.
This reason is likely to cover many of your data processing requirements while they are managing a lease.