All you need to do is, either start you're new log book where the old one left off, or as you're on you're ppl transfer the whole lot over to the new one. You have to keep the old log book though as it will have you're sign offs, hours and checkrides in etc.
Then when you have to submit the log book to the authority for license issue/rating you need to send both the old and the new one in together.
Just make sure you keep the old one.