delay, postpone, defer

延期する
delay: 後ろにのびのび　というイメージ
postpone: 予定されていた行事を、後のある日に置きなおす　というイメージ
defer: 権限を持っている人が予定を先送りするイメージ。公式な会議が延期されるときに使われる

The bus was delayed by an hour because of the heavy traffic.
We had to postpone the trip because of the typhoon.
He decided to defer the meeting to a later date because half of his subordinates were absent from work due to sickness.