incoming prime minister; prime minister-designate
Refers to the person expected to become the next prime minister, typically after an election or party leadership change, before officially taking office.
The candidate chosen as the incoming prime minister held a press conference.
Attention is focused on the policy direction of the prime minister-designate.
首相 is the current prime minister, while 次期首相 specifically refers to the person expected to become the next prime minister.
次期大統領 is the equivalent term for an incoming president, used in presidential systems.
Compound of 次期 (じき, 'next term') and 首相 (しゅしょう, 'prime minister').