A Lawyers Liability Policy is a “claims made” insurance policy. Once coverage ceases, so does your coverage for your past acts. This is unlike an “occurrence” policy, such as a Business Owners Policy, where if you let the coverage lapse for a few days and start another policy there is only a gap in coverage for the days that the “occurrence” policy was not in force. But with the "occurrence" policy you do not loose coverage for the time you had coverage inforce.
Your alternatives dwindle the longer the Lawyers Professional Liability coverage is not in force:
1. If just a few days, might find a carrier that is willing to backdate and pick up your prior acts, or your old incumbent carrier is still willing to renewal. This is your best option.
2. If more than a few days (up to 30 or 60 days), likely best alternative if you can is to purchase the Extended Reporting Endorsement (ERP/Tail). And then obtain a new Lawyers Professional Liability Policy without prior acts.
3. If past acts are not a big concern, then obtain a new Lawyers Professional Liability policy without prior acts.
4. If you are outside of the timeframe to purchase the ERP on your Lawyers Professional Liability policy, there might be some options with surplus lines carriers to pick-up your prior acts and write a policy for you. But this is a expensive option.
So the morale of the story is letting your Lawyers Professional Liability policy lapse is a big deal.