Liberty Insurance has said it will offer motor customers rebates of €5m as a result of the reduction in claims due to the Covid-19 restrictions.
Each customer will receive 15% of their existing premium for two months, provided this reaches a minimum amount of €10.
However, for practical reasons customers will have to request rebates, beginning on June 8 via the insurer's website.
Customers can either claim the refund through a "cash equivalent voucher" or they can ask the company to donate it on their behalf to a charity assisting with the frontline response to Covid-19.
If the money is not collected during the timeframe, each customer's entitlement will be given to charity.
The measure does not apply to fleet policies.
"We recognise that these are exceptional circumstances and now is a challenging time for many of our customers. We also recognise that risks on Irish roads are reduced in light of current restrictions," said Tom McIlduff, CEO of Liberty Insurance
Other insurers have also begun the process of offering rebates to customers following the decision last week by a number of companies to agree to discount premiums or give refunds to customers in recognition of an expected reduction in the volume of claims during the Covid-19 emergency.
Axa says it is putting in place a rebate or refund package worth up €20m for its 600,000 customers.
It is understood the measures could be worth approximately €30 per customer on average.
No timeframe has been set yet for the commencement of the rebates, but it is likely to be a couple of weeks.
It is not yet clear how Axa will operate the refund system.
Meanwhile, insurance company RSA said it will be communicating with its motor policyholders in the coming weeks.
In a statement, the insurance company said that it recognises that this is a challenging time for many of its customers, adding that it will play its part in providing whatever supports it can.
"We have already introduced extensive measures to help our personal and business customers, and will be communicating with our motor policyholders in the coming weeks," the statement added.