Handle the insurance before the boxes are unpacked. A move is one of the few events that changes the price, the required coverage, and sometimes the company willing to write the policy, all at once. Keeping the old policy and assuming it will follow you to the new address is the most common way to discover a problem at the worst possible moment.
Why a ZIP code rewrites the estimate
The garaging address is a rating factor, not a mailing preference. Traffic density, theft and weather claims in an area, repair costs nearby, and the number of uninsured drivers all feed into the price attached to where the car sleeps. Two neighborhoods a few miles apart can produce noticeably different totals for the same driver and the same car. That is also why an address left unchanged after a move is a problem: the policy was priced for a place the vehicle no longer is.
Tell the carrier the exact date the car began living at the new address. Some will adjust the premium mid-term and issue a small credit or charge; others will quote a fresh policy. Either way, the correct address needs to be in the file before a claim happens, not reconstructed afterward.
Crossing a state line is a different job
Moving within a state is usually an address change. Moving between states usually means a new policy, because minimum limits, no-fault rules, uninsured motorist requirements, and the forms filed with the insurance department belong to the state where the car is registered. A policy written in one state may not be valid or sufficient in another, even if the carrier operates in both.
Expect a sequence rather than a single phone call: new policy, new proof of insurance, vehicle registration, and then a driver's license update on whatever timetable the new state sets. Cancel the old policy only after the replacement is active and the registration office has accepted your proof. Many households get the order backwards and end up paying for two policies briefly, which is far cheaper than a lapse.
What to tell the new carrier
Give the exact new garaging address, the date of the move, an honest annual mileage estimate, and every household member who will drive. If the commute changed, say so. If the car is financed or leased, mention the lienholder, since the required physical damage limits and the deductible ceiling often come from that agreement rather than from your own preference.
Ask for a written declarations page and a fresh insurance card before you visit the registration office. A screenshot of an application is not proof of an active policy, and a clerk at a counter is unlikely to accept it.
Timing and the risk of a lapse
Start two to three weeks ahead of the move if you can. That leaves time to compare a few estimates with matched coverage, to get the lienholder's details onto the policy, and to correct a wrong VIN or a misspelled street name. A single day without coverage can trigger a notice from the motor vehicle agency, a higher price at the next application, and no protection at all if the moving truck is hit on the way.
One last detail people miss: update the address on every policy you hold, not just the car. Bundled home or renters coverage is often priced from the same location, and a mismatch between the two files tends to surface during a claim rather than during a routine review.