The better practice is to let your parole officer know that this offense occurred before your last incarceration. Take a copy of the new sentence and even a copy of the accusation/indictment so that they can see that this was before you were placed on parole. Being on probation and parole at the same time is not easy. Do not get your report dates mixed up.
YES! You absolutely need to tell your parole officer everything so they don't find out on their own and think you are hiding things from them! If it is for an old charge, they will understand. If you don't tell them and they find out on their own, they are a lot less likely to understand.