India, Feb. 28 -- A former rapper who ran Kathmandu as a mayor. The young leader of Nepal's oldest political party. And a communist veteran politician hoping to return to power after being ousted in youth-led protests in which dozens were killed last year. They are the three leading contenders as Nepal heads into a crucial nationwide election, the first since the protests led to the fall of former Prime Minister Khadga Prasad Oli's Government in September.

Whoever prevails will become Nepal's 16th prime minister in less than two decades, underscoring the recurring political instability that has marked the Himalayan nation since the monarchy was abolished in 2008. The protests in Nepal last year revealed the extent of young people's frust...