Collocations for presidency - noun

executive
vice (AmE) (vice-presidency in BrE)
He became a candidate for the vice presidency.

rotating
Greece then held the rotating presidency of the European Union.

one-term, eight-year, two-term, etc.

be nominated for, run for, stand for
be elected to, win
assume, take on, take over
hold
She held the presidency of the association for three years.

resign
That year he resigned his presidency of the Academy.

into sb's presidency
Three years into his presidency, he is more popular than ever.

under sb's presidency
under the presidency of Gerald Ford