The book of Hebrews is contrasting the old covenant with the new covenant, the worldly or earthly covenant with the heavenly or spiritual covenant of the heart under the gospel of Christ. The old covenant was about to pass away when the book of Hebrews was written, approx. AD 60 -65.
"In that he saith, A new covenant, he hath made the first old. Now that which decayeth and waxeth old is ready to vanish away." (KJV)
The author (probably Paul) was reminding them that when the temple was destroyed the old Mosaic animal sacrificial system would be finally taken out of the way. It had been legally taken out of the way at the cross, when Christ became the Lamb slain from the foundation of the world (Rev. 13:8).
Because Yeshua's (Jesus') sacrifice became the only sacrifice that would ever more be acceptable to God (YHVH) (Heb 9:12; 10: 26), all of the animal sin sacrifices became obsolete, unnecessary, and profane.
Heb. 9:1-5, continues immediately after Heb. 8:13 pronounces the passing away of the temple worship service, the old covenant service.
"Then verily the first covenant had also ordinances of divine service, and a worldly sanctuary.
2 For there was a tabernacle made; the first, wherein was the candlestick, and the table, and the shewbread; which is called the sanctuary.
3 And after the second veil, the tabernacle which is called the Holiest of all;
4 Which had the golden censer, and the ark of the covenant overlaid round about with gold, wherein was the golden pot that had manna, and Aaron's rod that budded, and the tables of the covenant;
5 And over it the cherubims of glory shadowing the mercyseat; of which we cannot now speak particularly." (KJV)
The ordinances were further defined in Heb. 9:10-12,
"10 Which stood only in meats and drinks, and divers washings, and carnal ordinances, imposed on them until the time of reformation.
11 But Christ being come an high priest of good things to come, by a greater and more perfect tabernacle, not made with hands, that is to say, not of this building;
12 Neither by the blood of goats and calves, but by his own blood he entered in once into the holy place, having obtained eternal redemption for us." (KJV)
All of the ordinances that were provided for the care of the temple, the priestly courses, the animal sacrifices, the incense offerings (the sweet orders), the purification rituals were all looking forward to the final and last sacrifice which Christ fulfilled in AD 30-31.
"The holy portion of the land shall be for the priests the ministers of the sanctuary, which shall come near to minister unto the Lord: and it shall be a place for their houses, and an holy place for the sanctuary." (KJV)
"17 And it shall be the prince's part to give burnt offerings, and meat offerings, and drink offerings, in the feasts, and in the new moons, and in the sabbaths, in all solemnities of the house of Israel: he shall prepare the sin offering, and the meat offering, and the burnt offering, and the peace offerings, to make reconciliation for the house of Israel.
18 Thus saith the Lord God; In the first month, in the first day of the month, thou shalt take a young bullock without blemish, and cleanse the sanctuary:
19 And the priest shall take of the blood of the sin offering, and put it upon the posts of the house, and upon the four corners of the settle of the altar, and upon the posts of the gate of the inner court." (KJV)
All of these ordinances contained in the law were in observance of and by command of God for His earthly temple to reconcile the people to Him through the sin offerings.
When Gabriel told Daniel that the end of desolations of Jerusalem would accomplish 6 things in Dan. 9:24,
"Seventy weeks are determined upon thy people and upon thy holy city, to finish the transgression, and to make an end of sins, and to make reconciliation for iniquity, and to bring in everlasting righteousness, and to seal up the vision and prophecy, and to anoint the most Holy." (KJV)
all of them were accomplished in Christ, fulfilled in Christ at His death on the cross. The making an end of sins referred not to an end of man's sins, but the end of the animal sacrifices and offerings for sin. (1)
Therefore, Paul said in Eph. 2:15-16,
"Having abolished in his flesh the enmity, even the law of commandments contained in ordinances; for to make in himself of twain one new man, so making peace;
16 And that he might reconcile both unto God in one body by the cross, having slain the enmity thereby:" (KJV)
The commandments contained in ordinances were the very same ordinances of divine service of the worldly sanctuary spoken of in Heb. 9:1. They were all of the "fence" ordinances surrounding the 10 commandments that were established for the service of the temple and the sin offerings.
Christ is now the sin offering. There is no other offering acceptable to God, and therefore the statement at Heb 10:18,
"Now where remission of these is, there is no more offering for sin." (KJV)
There is no need for the ordinance of the earthly temple sanctuary that was under the old covenant because God annulled it through Christ Yeshua's sacrifice (Heb 7.18).
That is why there is no more need for any earthly temple, nor any animal sacrifice system, nor any ordinances governing them. They are all fulfilled in Christ.
They were part of the old covenant, not distinct from it. These are the part of the old covenant that were waxing old and about to pass away in the first century AD. At the destruction of the temple in AD 70, the temple was burned along with all of the genealogical records, and the Romans tore it down and razed the walls of the city (2) (3).
All bold emphasis is mine.
(1) Daniel and The End Times ShreddingTheVeil
(2) Josephus Visual Timeline here
(3) The Signs of The Feasts - Part II ShreddingTheVeil