LONDON, Nov 4 (Reuters) - Insurers could face European climate stress tests as soon as 2023, the head of the EU"s insurance regulator said at the Reuters Future of Insurance Europe conference on Thursday. The insurance industry faces exposure to climate change risk both through its underwriting of fossil fuels and through the investment portfolios of individual insurers. Petra Hielkema, chairperson of the European Insurance and Occupational Pensions Authority (EIOPA), said although the tests will take place by 2024 at the latest "it might be we want to do this one quicker". But Hielkema, who was speaking on a panel on climate change, said there was "no concrete planning" for 2023 tests yet. Hielkema said stress tests for pension funds next year were also likely to focus on climate change. Anna Sweeney, the Bank of England"s executive director for insurance, said the central bank was in the process of conducting its first climate stress tests for banks and insurers, with results due in the first quarter of 2022. "We"ve had to ask for resubmissions from some firms where we have felt that there hasn"t been enough due diligence...or enough clarity," she told the panel. Hielkema and Sweeney both said their tests would not be focused on capital requirements. Hielkema said the use of a carbon tax was a better way to encourage companies to tackle climate change risk than imposing capital requirements. Alison Martin, EMEA CEO for Zurich Insurance (ZURN.S), also told the panel that a carbon price was needed "as part of a suite of mechanisms to help us get to the transition". "We have nearly 70 different versions of carbon price mechanisms...there"s a challenge to get to something which is harmonised," Martin said. Delegates at the U.N. climate conference in Glasgow are wrangling over the rules around Article 6, the section of the U.N. Convention on Climate Change that deals with markets for trading carbon emissions that continue to be emitted. One of the toughest tasks will be in synchronizing global rules around these markets, as well as in agreeing on a global price for carbon. read more Marie Niemczyk, head of insurance relations at investment firm Candriam, told the panel that a carbon price would be a very useful tool in investing, but "it needs to be high enough to actually have a deterrent effect". For more on the Reuters Future of Insurance Europe conference please click here Reporting by Carolyn Cohn and Huw Jones; Editing by Kirstin Ridley and Alexander Smith