We had insurance for AirPods which lost. If we buy a new pair, can we apply the AppleCare to the new AirPods?

AFAIK, Apple's Theft and Loss coverage only applies to the iPhones; whereas, their AppleCare+ plan does cover the AirPods and would incur a reduced cost for replacement.

Ref:

• Apple HomePod, Headphones, AirPods, or iPod touch - Apple
• Replace your AirPods - Apple Support

If you lose the case and both Airpods it is actually cheaper to buy a new set rather than going through AirPods Repair. But I believe they are asking about transferring the AppleCare + from the original pair they bought towards the new ones they are buying.

Call AppleCare regarding how this can be handled.