Imran Khan (2018-22) on Apr. 10 became the first prime minister in Pakistan’s history to be ousted through a parliamentary vote of no confidence. But this is only part of the story. No democratically elected Pakistani prime minister has ever completed a full term in office. As such, the fate of the Khan government is a reoccurring tale in Pakistan, only this time told in a different way.

The coming to power of new Prime Minister Shehbaz Sharif portends possibly significant consequences for the country’s foreign policy. For Iran, Pakistan’s western neighbor with which it shares a 909 km (565 miles) border, the political developments in Islamabad are a mixed bag...