When you cancel your insurance policy with your current insurer, shortly afterwards they will send you a document showing how much no claims bonus you have acquired. You normally have to send this document to your new insurer as proof of the no claims discount you're entitled to.
After you've completed a year with the new insurer, you will then
earn another year's no claims discount on top of what you have. So your total no claims bonus will become 3 years (1 year from new insurer + 2 years discount from previous insurance company). If you then decide to move to another insurance company, you will be able to transfer 3 years no claims and the cycle will continue as long as you don't claim on your car insurance policy.