3 points on provisional licence, will they show when I pass my test?

The points will be carried forward on your new full driving licence unless they have expired. Depending on the type of offence you committed on your provisional, penalty points can stay on your licence for a maximum of 11 years. From the looks of it though (because you said you got 3 points), it might have been for a minor offence which means that the points will stay for 4 years on your licence and since it's been over four years now, they might be removed. If you can confirm which offence you got the penalty points for, then I could tell you for sure.