The second appearing in Hebrews 9 is not the Rapture, but Christ’s second appearing to Israel.
We spent five lessons on the Day of Atonement in Leviticus 16. But let’s think about its future fulfillment. “Christ has not entered the holy places made with hands, which are copies of the true, but into heaven itself, now to appear in the presence of God for us;…but now, once at the end of the ages, He has appeared to put away sin by the sacrifice of Himself. And as it is appointed for men to die once, but after this the judgment, so Christ was offered once to bear the sins of many. To those who eagerly wait for Him He will appear a second time, apart from sin, for salvation” (Heb 9:24-28). Do you see the three appearings? The high priest took the bull’s blood in for the priesthood, and we, though Gentiles, having accepted Christ’s death by faith become God’s priests, believing Messiah is now in God’s presence for us. The second time the high priest appeared, it was with goat’s blood for the people. So Christ will yet appear to Israel and “In that day a fountain shall be opened for the house of David…, for sin and for uncleanness” (Zech 13:1). Notice, His next appearing to Israel will be “apart from sin.” No need to provide another sacrifice of Himself! But it will be “for salvation.” How many will respond in faith, and how many “not afflicted in soul on that same day shall be cut off from his people” (Lev 23:29)? “Two-thirds in it shall be cut off and die, but one-third shall be left in it…They will call on My name, and I will answer them. I will say, ‘This is My people’; and each one will say, ‘The Lord is my God’” (Zech 13:8-9). What a glorious day when “all Israel will be saved” (Rom 11:26). Israel will yet say, “We esteemed Him stricken, smitten by God, and afflicted. But He was wounded for our transgressions…” (Isa 53:4-5). And then Christ will “be satisfied” (v 11).