OTTAWA—Mark Carney took over Friday as Canada’s prime minister, planting a former central banker known for navigating crises in the middle of a trade war with President Trump and likely kicking off a national election. 

Carney, who turns 60 years old Sunday, succeeded Justin Trudeau, who resigned under pressure from poor polls. His immediate task is resolving a crisis over tariffs with the U.S., which has imposed 25% tariffs on steel, aluminum and goods that don’t comply with Canada and the U.S.’s free-trade agreement, plus 10% on Canadian crude imports.