The answer is on another thread, but I cannot remember the heading at the moment. From memory when I did this in 2015 .... If you are in Lima, just take your passports to Immigraciones, go to Informes (Point number one) and tell the person there. You will get a slip with a number on it and when the number comes up on the screen, go to the said counter. They will give you a small slip to fill out and point you in the appropriate direction. When I did this, I went to point three by the staircase. (Point two is for Peruvian Passports.)
Show them the slip, they will give you a number (same system as point one) and probably direct you to the third floor. Sit and wait till your number comes up on the screen and go to the said numbered counter and hand your information over. They will do their bit on the computer changing your passport number on their screen and stamp your Carnet number into your new passport. You will have to wait another 4 or 5 minutes then your name is called and you will receive everything back.
If you do not need a new Carnet, all over and done with.
However, these days, many of the Carnet details are dealt with at the booths in the car park along side the waiting room. If this is the case, they will send you to that section and there will be a person there with slips as well and then follow the same system.
Took me about 20-30 minutes from start to finish
If you are not in Lima, can't help you.