Okay, if you're making a claim that's a slightly different matter.
An insurance policy covers you for a certain period of time (usually stated as X date to midnight on Y date). In return for that coverage, you agree to pay a premium. Let's say the period for Policy A is stated to be from 1 November 2018 to midnight on 31 October 2019. That means you're covered for a claimable event during that period. If it happens outside that period, e.g. on 1 November 2019, then you're not covered under Policy A's period.
The next year (1/11/19 to midnight on 31/10/20) is Policy B's period. It doesn't matter whether it's the same insurer or a different one - it's a new policy of insurance. It's actually easier if you imagine you swapped insurers. If you make a claim for an event under Policy B, but haven't paid the premium for that period, you're effectively asking for an insurance payout without any cost to you. In a sense, 'free insurance'. It doesn't work like that.
Where you make a claim, insurers are entitled to payment of the full insurance premium for the policy period. They've agreed to cover you for the insured risks, and you've agreed to pay the set premium. Very simply: If you don't pay the premium, they don't have to provide the cover.