"Plate" means "number plate" or "registration number plate", the identifying mark on the front and back of all cars. I'm not sure if "cold" here means "it doesn't exist so it must be a fake" or "it shows up as stolen". I'm sure an AmE speaker will be able to clarify that.
His partner ensures that he definitely checked the correct set of letters and numbers and when he says that he is sure, his partner says that it's now time to switch on the red and blue flashing lights on top of the patrol car, to indicate to the other driver that he must stop.
Student or Learner