All the vaccines on the National Immunisation Schedule can now be given concurrently, immediately before or after the mRNA-COVID-19 vaccine, Comirnaty, with the exception of the shingles vaccine (Zostavax). This includes MMR, influenza, HPV (Gardasil 9), tetanus, diphteria and pertussis (Boostrix) and the meningococcal vaccines (Bexsero and Menactra). See the IMAC COVID-19 website, here, for further information.
To ensure a good immune response in older adults, spacing of at least 7 days is recommended between Comirnaty and Zostavax. There are no safety concerns if this timing is not possible.