Since you have been on bc for a year now, then there is no reason to use extra protection against pregnancy (condom ur choice). Starting a new pill pack every month, your protected from month to month, even when u are not on the active pills.
Usually if you're taking the pill for the very first time you will be advised to wait 7 days before having unprotected sex. Although, if by 'new pill pack' you just mean the first pill after your period, the pill will still be effective from the previous 28 days.