To actually "delete" a domain would probably require an extraordinary effort. Most registrars don't even have this option, at least in their online interface. You'd probably have to call them on the phone, and then they'd have to figure out just how to do it!
You can let the registration expire, but then there is a grace period, and it will still work through the grace period. And even then, once it is "shut off", it is usually held for an additional period before it will be re-issued to somebody else. Some registrars will attempt to re-sell expired domains at a premium price in the secondary market, if they feel it has value. So, a very risky thing to do (allowing it to expire).
As others have stated, transfer it. You initiate the transfer from the NEW registrar. You will most likely have to supply a code that you will need to get from your existing registrar.
BTW, when you transfer, you will keep the remaining portion of your registration period, plus whatever period you registered with at the new registrar. Say, you had already paid for a 2-year registration, and only 6 months have gone by. Transfer to a new registrar with a 1-year registration period, and you are good for 2 1/2 years.