In Australia P plates which are new drivers are not allowed to drive turbo cars is it possible to remove a turbo from a car and leave it off with the car able to function?

you can, depending on the type of fuel system the car has. If there is a non-turbo equivalent you can change the fuel system and manifolds and it would run but would go like a pig because most turbo motors have low compression to cope with boost. If no non-turbo equivalent you could spend a lifetime making it all work properly. It's not really a very good idea, just get a non-turbo until you get off your Ps.