Does the book of Hebrews say the Mosaic covenant is obsolete?

Yes, explicitly. Hebrews 8:13 uses the perfect active indicative 'pepalaiken' — a completed action with ongoing results — to say that by calling the covenant 'new,' God declared the first permanently obsolete, with no grammatical allowance for future reinstatement.

Yes, explicitly — and the grammar of Hebrews 8:13 doesn't leave any wiggle room.

"In saying 'new,' he has made the first obsolete. And what is becoming obsolete and growing old is near to vanishing." — Hebrews 8:13

The verb here, pepalaiken (πεπαλαίωκεν, G3822), is a perfect active indicative in Greek. That tense describes a completed action whose effects are still in force — like saying "the door has been opened" when it's still standing open. The author's logic is precise: the very act of God calling a covenant "new" in Jeremiah 31 was itself the declaration that the previous one was obsolete. You don't need a "new" thing unless the old thing is being replaced.

The author of Hebrews had just quoted Jeremiah 31:31–34, the only place in the entire Hebrew Old Testament where the phrase berit chadashah (בְּרִית חֲדָשָׁה, "new covenant") appears. Jeremiah 31:32 is specific about what changes: "Not like the covenant I made with their fathers." But the difference isn't the people — the new covenant is still made with Israel. The difference is the mechanism. The Torah that was on stone tablets will now be written on the heart (Jeremiah 31:33; see also Ezekiel 36:26–27).

What this means is that the new covenant isn't replacing the relationship — it's fulfilling it through a new and better administration. The covenant formula of Jeremiah 31:33 ("I will be their God, and they shall be my people") is identical to the formula in the Abrahamic covenant (Genesis 17:7) and the Mosaic covenant (Exodus 6:7). Same relationship, different mechanism. And Jeremiah 32:40 calls this new covenant berit olam — "everlasting covenant" — the same label attached to the Noahic, Abrahamic, and Davidic covenants.

The Mosaic covenant was conditional — built on "if you obey" (Exodus 19:5) — and Jeremiah 31:32 says plainly that Israel broke it. The Abrahamic promise was unilateral and unconditional. The new covenant is the fulfillment of the unilateral promise, not the revival of the bilateral one.

For the full argument and the Hebrew and Greek texts of Jeremiah 31, see the study on One Plan, One People, section "The New Covenant: The Old Made New."