Passage
we have an altar, of which to eat they have no authority who the tabernacle are serving,
we have an altar, of which to eat they have no authority who the tabernacle are serving,
Hebrews 13:8 Jesus Christ yesterday and to-day the same, and to the ages;
Hebrews 13:9 with teachings manifold and strange be not carried about, for <FI>it is<Fi> good that by grace the heart be confirmed, not with meats, in which they who were occupied were not profited;
Hebrews 13:10 we have an altar, of which to eat they have no authority who the tabernacle are serving,
Hebrews 13:11 for of those beasts whose blood is brought for sin into the holy places through the chief priest--of these the bodies are burned without the camp.
Hebrews 13:12 Wherefore, also Jesus--that he might sanctify through <FI>his<Fi> own blood the people--without the gate did suffer;
The verse centers on "altar", "authority", "tabernacle", and "serving". It is saying that the verse draws attention to "altar" and "authority", so its meaning should be read from those terms before moving to application.
The nearby context moves from verse 9's "with teachings manifold and strange be not..." into verse 11's "for of those beasts whose blood is...", so "altar" and "authority" belong inside that flow. In Hebrews context, the local focus is Christ, faith, and discipleship.
A plain takeaway is to answer the verse's own emphasis on "altar" and "authority" with trust shaped by these words, not by a vague optimism outside the passage.