If you want to start a new character, your old one will have to die through in-game means (i.e. be executed or fly into a sun). After a 3-week waiting period, you will be allowed to create a new character.
You can't "delete" your account the only way to get rid of your character is to either fly a ship your in into a sun or have someone arrest and execute you. Then after your character is dead you will have to wait three weeks until you can make a new one