Very few car lease contracts include insurance, so you’ll likely need to arrange this yourself.
When leasing, you must take out fully comprehensive insurance for the duration of the contract.
When you take out an insurance policy, you’ll need to let the insurance provider know that it’s for a leased car. You'll need to share the terms of the lease, alongside the name of the car’s registered owner (normally the lease company) and the names of any additional drivers.
You may also want to consider ‘gap insurance’. Gap insurance protects against any difference there might be between the insurance company pay-out if your car is written off and the amount left to pay on your lease.