Yes, if you move, you need to notify the IRS of your new address. We can change our records so that any tax refunds due to you or any other IRS communications will reach you in a timely manner.
Submit Form 8822, Change of Address, to request an address change.
Caution If you are a representative signing on behalf of the taxpayer, you must attach to Form 8822 a copy of your power of attorney. To do this, you can use Form 2848. The Internal Revenue Service will not complete an address change from an "unauthorized" third party.