You can buy a new domain anytime you would like. You can change the configuration of your new domain to act as a easier access to your long URL. You will still have control over your current domain until the term expires. You can choose to cancel the domain and it will be removed from your account but there is no real reason to do that.
In my experience you should keep a sunsetting domain for a period of time while you introduce a new domain. You wouldn't want someone to go to the domain they have become accustomed to and not be able to contact you. If you (as an example) have six (6) months left on your current domain I would use the remainder of that time to inform visitors of your domain change. Additionally if you are going to get rid of your domain check that the auto-renew is not active. I hope that helps?
...turns out that my two cents is worth less or more depending on the current exchange rate.
roy darling *my posts seem a lot shorter in my head