Full trading on the stock market began on 15 October, and Instinctif is continuing to provide PR support on an ongoing basis.
The agency was appointed to the brief following a competitive pitch, although Instinctif had already worked with the company for several years helping with its quarterly bond reporting.
Hastings is aiming to raise £180m through the IPO to pay off some outstanding debts.
In a statement announcing plans for the flotation, Hastings said it had a 5.5 per cent share of the UK private car insurance market, looking after 1.88 million customer polices.
Hastings Group CEO Gary Hoffman said: "We are delighted to have Instinctif as part of our core advisory team. It provided straightforward advice to our colleagues across the business and helped us navigate volatile markets in achieving a successful IPO."