Eldar was previously CEO of Equinor ASA (formerly Statoil), the largest oil and gas group on the Norwegian continental shelf and a major global energy company with presence in more than 30 countries. Currently, he is Chair of Strømberg Gruppen AS, Vartdal Holding AS and an Independent Director of Subsea 7 SA and Fjord Base Holding AS. Eldar is currently also Chair of the Advisory Board of Vard Group AS and adviser to Nysnø Climate Investments (owned by the Norwegian Government).

Eldar was appointed President and CEO of Statoil/ Equinor in 2015 (acting in the role from 2014). He was instrumental in transforming Equinor into a broader energy company focused on low-carbon strategies and new-energy solutions.

Eldar joined Statoil in 1980 and held several management positions in the company, mainly in the fields of accounting and finance. He was Executive Vice President and CFO from October 2003 to December 2010, when he became Executive Vice President for Marketing, Processing and Renewable energy (MPR). In MPR, he had responsibility for all downstream and marketing/trading, midstream and renewable-energy activities.