Complex sentence: In 1999 she served as a broker across the frosty relations between the retiring Moynihan and Hillary Clinton, who would successfully gain his seat in the 2000 New York senatorial election.
Split into simpler sentences: In 1999 she served as a broker across the frosty relations between the retiring Moynihan and Hillary Clinton. The latter would later successfully gain the former's seat in the 2000 New York senatorial election.