There is no central repository for employment records in Canada. Private companies retain their own personnel files, usually disposing of older ones after a certain period of time. Some deposit older company records with an archives in the area or maintain their own archives. To determine if employment records have survived, you must first determine if the company is still in existence, and if so, contact them regarding their holdings.
Library and Archives Canada holds archival records of some private companies and organizations, which may or may not include records relating to employees. If you know the company name, you can search the Archives Search database.
Some companies deposit their archival records in the Provincial and Territorial Archives in the province or territory where the company operated.
To search the holdings of other archives in Canada, consult the Canadian Council of Archives portal: ArchivesCanada.ca.