Levesque, leader of the Official Opposition in the National Assembly of Quebec.
In 1979, he was elected to the National Assembly as a Liberal Party candidate in a by-election in the riding of Jean-Talon.
He was re-elected in the 1981 general election.
He was appointed to the Senate on the recommendation of Prime Minister Brian Mulroney in 1993.
He initially sat as a Progressive Conservative Senator.
Upon that party's merger with the Canadian Alliance, he sat in the newly formed Conservative Party caucus.
In September 2004, he changed his designation to "Independent".
He was a member of the Senate Legal and Constitutional Affairs committee.
Rivest retired from the Senate at the end of January 2015, three years prior to reaching the mandatory retirement age of 75.