A service contract is only useful if the provider can reach you. The contract spells out what the provider owes and what you owe. It also usually says how the two of you talk to each other, and that part gets ignored until a notice goes to an old address and nobody sees it.
Where the notices go
Find the section on notices or communications. It will name a method, such as letter, email, or the provider's online account, and it will say which address the provider uses for you. Some contracts treat a notice sent to the last address on file as delivered, even if you never saw it. That is a rule to understand before you move, not after.
Ask the provider how you can see the contact details it holds for your contract. Ask whether you can change them yourself online or by writing to the company, and whether a change needs proof of your new address. Keep the confirmation.
Events that change the contact details
Most people update the address when they move house. Fewer update the other details: a new phone number, a new email, a changed name after a marriage, or another adult who now drives the car. Any of these can matter if the provider needs to send a renewal offer, a cancellation notice, or a request for paperwork during a claim.
When the car changes hands, the contract belongs to the contract holder, not to the car. Check what the contract says about who receives notices after a transfer. Do not assume your details simply replace the seller's.
What to keep
Keep a copy of the notice clause with the contract itself. Keep the provider's contact line and your contract number somewhere you can find them without digging through the glovebox. Whenever your details change, send the provider a short written update and keep proof that it arrived. A letter returned to the provider can turn into a lapse you never saw coming.
To see how notice and transfer rules are written before you have a problem, read a sample contract. Several providers post one, and the table of companies that publish a sample contract is a good place to start.