While a formal EICR isn’t always a strict requirement for a consumer unit replacement, it is highly recommended and best practice to ensure the existing installation is safe and suitable for the upgrade. Replacing the consumer unit requires completing an Electrical Installation Certificate (EIC) to certify the new unit itself, but the EIC does not cover the condition of the entire installation, which is the purpose of an EICR. An EICR is essential to identify any underlying issues in the wiring that could cause problems or pose a safety hazard after the new consumer unit is installed.
As long as you have an EICR saying the installation is inspected and tested satisfactory against the latest edition of the wiring regulations that is all you need but for the avoidance of doubt supply a copy of the EIC to the tenant or, if it is a new tenancy, attach a copy of the EIC to the EICR.
Further Reading
Can I use an EIC instead of an EICR to comply with the electrical safety regulations?