Quelch first ran for public office in the 1935 Canadian federal election as a candidate from the Social Credit Party of Canada in the Acadia district in Alberta.

In one of the closest contests in that election, he retained his seat by a margin of 27 votes, defeating Liberal candidate Arthur Day, whom he had previously faced in 1935.

In 1950, Quelch was appointed by Liberal Prime Minister Louis St. Laurent to serve as one of six members from all parties as a Parliamentary adviser to the Canadian staff to the United Nations Assembly.

Over his 23 years of service in the House of Commons of Canada, he served as critic for finance, agriculture, and fisheries.

Quelch died of pneumonia in September 1975[3] but, due to an oversight, no tribute was paid to him as was custom with deceased former members from the Canadian House of Commons.