Past Projects (in Consultancy) shown in New Personal Company

This might be true but in this case the “creator” wouldn’t be you but rather the consultancy you worked for.
So if there are photos, renders or any other promotional assets, my guess would be that they could probably tell you to not show it on your website.
This is why it would be important to get their ok or put it up and be ready to take it down if you are being told to do so.