OTTAWA — The race to replace Canadian Prime Minister Justin Trudeau is dominated by one name: Donald Trump. How to wrestle with the incoming president and his tariff threats has emerged as the defining question in the Liberal Party leadership contest.

Chrystia Freeland, the former deputy prime minister, sought to distance herself from Mr. Trudeau in a public letter criticizing him for “costly political gimmicks.”

Chrystia Freeland, whose abrupt resignation as finance minister last month forced Justin Trudeau's exit as prime minister, said she is running to be the next leader of the Liberal Party and prime minister of Canada.