Complex sentence: When Labour won the 1997 general election, Brown became Chancellor and Balls continued to work as his economic adviser; he went on to serve as Chairman of HM Treasury's Council of Economic Advisers.
Split into simpler sentences: When Labour won the 1997 UK general election, Brown became Chancellor and Balls continued to work as his economic adviser. He went on to serve as Chairman of HM Treasury's Council of Economic Advisers.