Hebrews argues that by speaking of a “new” covenant, God has made the first one old. It adds that what is becoming old and growing aged is ready to vanish away (Hebrews 8:13). The conclusion is drawn directly from the wording “new.”
Hebrews 8:13 draws a conclusion from the earlier quotation about a “new covenant.” The writer argues that calling it “new” automatically frames the earlier covenant as “old.” Then the writer adds a picture: what is already becoming old and visibly aging is close to disappearing. This single verse functions like a closing takeaway for the discussion in Hebrews 8 about covenant and priestly ministry. Just before this, the author quotes Jeremiah’s promise of a “new covenant” to show that Scripture itself anticipates change (Hebrews 8:8–12).
Hebrews 8:13 is the author’s drawn conclusion from Jeremiah’s promise of a “new covenant” (Hebrews 8:8).
A careful answer keeps the immediate passage, the book's argument, and the whole-Bible storyline together, so the question is answered in context instead of as a detached idea.
Start with Hebrews 8:13, then read the surrounding section so the answer stays connected to the passage's flow.
13In that he says, "A new covenant," he has made the first old. But that which is becoming old and grows aged is near to vanishing away.