Think of each save game as it's own universe. When you start a new game, it's a new universe without your previous sim's existence. If you want to continue in the same universe, then as the previous poster suggested, go into Edit Town, create your new sim, move them into a house or property and then choose to change households to the new one. Your previous sim will then be controlled by the computer, just like the other townies and continue to live their life.
You could even merge the new sim into your current household and play them both. Like if a cousin came to visit, or an old friend. That sort of thing.