Collocations for prime minister - noun

deputy
acting, caretaker, interim, transitional
incumbent, present
former, previous
outgoing
strong
beleaguered (esp. BrE)
The beleaguered prime minister is coming under more pressure.

Conservative, Labour, etc.

appoint, appoint sb (as), elect, elect sb (as)
serve as
He served briefly as prime minister from 1920 to 1921.

under a/the prime minister
She held office under two different prime ministers.