I would think insurance quotes last a few weeks, in fact probably days (if compare sites) rather than months. It’s best to as suggested call for quotes around 3 weeks before your renewal.
If you do get a good quote earlier then weigh up the pros and cons. Sometimes there’s a fee to cancel early with your current insurer and of course a refund on months not used. The closer you get to your renewal date it could cost you to cancel early rather than you end up with any monies back.
I had a refund on my MX-5 insurance this year, I had 6 months to run, surprisingly I got £109 back after the fee was deducted on a premium of around £350.