You will move before the end of 2024? When you prepare your 2024 tax return, you will enter your new address on that Form 1040--you will do that in MY INFO. But of course, use your new address on the W-4 too. A W-4 does not go to the IRS. It only goes to the employer to tell them how much tax to withhold.
Depending on what state you move to, you might need to prepare two different state tax returns for 2024---part year returns for each state. But we would need to know which states, since some states do not have income tax, and some states have reciprocal agreements.