Jann Brown, managing and finance director, and deputy chief executive Dr Mike Watts, both aged 58 and with a combined 35 years service, will step down as executive directors at next month's annual meeting, which already sees the departure of founder and chairman Sir Bill Gammell.
Ms Brown will work out 12 months notice on a salary of £362,675, a reduction of £75,000, while Dr Watts will work out six months on a salary similarly reduced to £400,600, but both will remain eligible for bonuses and long-term incentive awards.
James Smith, 37, the company's former adviser at Rothschild who joined Cairn last month, becomes finance director on a £350,000 salary along with a £200,000 "golden hello" compensation payment, half in cash and the rest in shares vesting after a year.
Ms Brown meanwhile will from May 15 also join the board of Wood Group, where she will take over the £60,000-a-year chairmanship of the audit committee.
Cairn said the moves were "long-term succession planning" and a restructure of the business, which would be reflected in a smaller board.
It said the departures had been planned before the lodging in January of a tax claim by the Indian government against Cairn which has wiped more than a third off its market value and stalled a £182m share buyback.
The shares, at 262p before the announcement in January, slipped 2.4p to 167.5p yesterday.
The company said: "Dr Watts and Ms Brown have agreed, during their notice periods, to continue in senior roles and dedicate their time to seeking to resolve the tax position in India." From May 15 two executive directors Mr Thomson and Mr Smith would be supported by exploration director Richard Heaton and chief operating officer Paul Mayland, who had a combined experience at Cairn of more than 30 years.
Mr Thomson, 49, said: "The changes announced today offer the best way of organising our business for the future - both in delivering our ongoing balanced growth strategy and in dealing with the situation in India." He thanked Ms Brown and Dr Watts "both for their instrumental contribution to the growth of Cairn over the years and for agreeing to remain in their new roles".
A Cairn spokeswoman added: "It is very good that we have their experience to dedicate to try to resolve the situation in India, because Jann was on the board of Cairn India for a number of years and knows the country and the politics well, while Mike was the exploration director."
She said investors viewed the slimmer structure as appropriate to what would be a smaller business after the eventual sale of Cairn India. The company's planned sale of its remaining 10.3 per cent stake to Vedanta Resources remains blocked by the Indian government, which faces an election in mid-May.
Vodafone and Shell have also been hit by retrospective tax demands from the Indian government under 2012 legislation.
In Cairn's case the demand relates to the £1billion flotation of Cairn India on the country's stock market in 2007. Cairn has said it has always complied with Indian tax law and will "take whatever steps are necessary to protect the company's interests".
Cairn raised £3.3bn from the sale of most of Cairn India in 2011, but a £600m exploration programme in Greenland has disappointed and last month Cairn reported a dry well in Morocco, where it acquired acreage through the £414m purchase of Nautical Petroleum in 2012.
Analysts at DeutscheBank said the company's asset value excluding the Indian disposal was around 200p a share, but a resolution in India was unlikely until the country's elections had run their course, and investors would also be watching exploration results from Senegal next month.