The Old Testament gives us the calendar. The New Testament gives us the verdict on what these days mean for the church.
For four of the appointed times — Passover, Unleavened Bread, Firstfruits, Pentecost — the New Testament names an explicit fulfillment, on the very day, in the events of Christ’s death, resurrection, and the founding of the church. For the others — Sabbath, Trumpets, Atonement, Booths — the NT speaks more broadly: Hebrews 4 (Sabbath rest), Hebrews 9–10 (Atonement), and the inferential resonances of Booths. Trumpets stands without a named fulfillment.
What Scripture does not do is build an elaborate end-time scheme on top of the unfulfilled feasts. The apostles’ one explicit teaching on the calendar for Christians is Paul’s:
Therefore let no one act as your judge in regard to food or drink, or in respect to a festival or a new moon or a Sabbath day — things which are a mere shadow of what is to come; but the substance belongs to Christ.— Colossians 2:16–17
Paul names the calendar — festival, new moon, Sabbath — and reads the whole of it as shadow. The substance is Christ. Where Scripture names a fulfillment in Christ, we read it gratefully. Where Scripture does not name one, we do not invent one.
The appointed times of the LORD are gifts. They taught Israel to mark the year by what the LORD had done; they pictured what the Messiah would do; and they pointed forward to a substance now arrived.