At present IIRC there is no internationally-recognised certificate of vaccination for covid. The vaccine isn't 100% effective. People who have been vaccinated can apparently still catch and transmit the disease.
People who have been vaccinated still have to follow all the "lockdown" regulations.
I suspect nothing changes until the risk has been reduced by having a substantial part of the population immunised and a properly functioning Test, Trace and Isolate system is in place.