Some car insurance providers will allow you to set a future start date. That means you could start earning your multi-car discount immediately and switch over when the time is right. Don’t forget to notify your current provider that you’re not renewing though.
Linked multi-car insurance policies will normally allow you to have different renewal dates for each policy, meaning you don’t have to try to sync all the renewal dates. But you should still get a discount for having more than one car insured with that provider.