Royal Bank of Scotland shares fell seven percent on Thursday after the surprise ousting of CEO Stephen Hester left investors questioning who would steer the part-nationalized bank through to an eventual privatization.

RBS said late on Wednesday Hester would step down by the end of this year. Its board decided it wanted new leadership to oversee the sale of Britain's majority stake in the bank, which could take years.

Chairman Philip Hampton will face a tough task finding a suitable replacement for one of the toughest jobs in British banking.

During his five years at the helm, Hester oversaw a massive shrinking of the bank's balance sheet all the while parrying criticism from politicians about the strategy and the size of his bonus.

"Hester is well respected and has arguably done as good a job as possible in very trying circumstances, given the difficult political and regulatory backdrop and the external pressures often placed on the bank," said Andrew Coombs, analyst at Citi.

Industry sources and analysts say the ideal successor would be an experienced banker used to dealing with lawmakers and regulators and untainted by recent banking scandals.

Only a small number of candidates would meet that criteria and Hampton admitted on Wednesday that there wouldn't be a large number of candidates on the shortlist.

By 3:50 a.m. ET RBS shares were down 5.4 percent to 307.9 pence after earlier dropping seven percent, underforming a 1.8 percent fall in the DJ STOXX Europe bank index <.SX7P> and far below the 407 pence price the government regards as the break even on its investment.

Britain pumped 45.5 billion pounds into RBS during the financial crisis, giving it an 82 percent stake in what was once the largest bank in the world by assets.

RBS said on Thursday it would further shrink its investment bank, which a source said will result in 2,000 more job cuts.

(Editing by Carmel Crimmins)