appointed time; fixed time
Refers to a predetermined or scheduled time, often with a nuance of a deadline or a specific moment that has been set. Slightly formal or old-fashioned; in casual speech 時間 or 時刻 are more common.
I was late for the appointed time of our meeting.
刻限が来たので、会議を始めましょう。
The appointed time has come, so let's begin the meeting.
刻限 shares the kanji 刻 with 刻み but means a fixed time or deadline, not a cut, notch, or interval.
Compound of 刻 (こく, 'time') and 限 (げん, 'limit'). The exact historical derivation is uncertain, but the combination naturally yields the meaning of a limited or fixed time.