In a sense, this means that we each stand alone. We are our own priests. This must have been a radical idea to those early Jewish Christians. Yet this is what Paul and Peter were driving at when they said things like: " Ye also are an holy priesthood, to offer up spiritual sacrifices...present your bodies a living sacrifice, holy, acceptable unto God, which is your reasonable (Gk. logikos) service (service is priestly language)" (1 Pet. 2:5; Rom. 12:1). They were saying: 'You're your own priest now!'. And the early believers found it hard to cope with. Have you considered that the most common form of apostasy (i.e. leaving the true Faith) in the early church was going back to the Jewish Law, with its system of priests? Natural Israel likewise totally failed to live up to God's desire that they should be a Kingdom of priests. They left it all to their priests. They didn't teach every man his neighbour and his brother, saying, Know the Lord (Heb. 8:11; even though when He re-accepts them, God will count them as if they did). Although it was God's original intention that each family leader sanctified themselves and slew the Passover lamb personally, they came to delegate this to their priests (so 2 Chron. 30:17 implies).
There are many allusions to the language of priesthood in the New Testament, both as major statements and also in passing (e.g. the description of us as " blameless" , Tit. 1:7, is priestly language). This usage illustrates for us the meaning of priesthood. " He that is washed needeth not save but to wash his feet" (Jn. 13:10) was surely suggesting that all baptized believers (" washed" ) were like the priests, who firstly washed their bodies and then their hands and feet, before entering on service (Ex. 30:21). Even the elderly brethren and sisters in Crete who were to be guided by specially appointed elders were to be encouraged to behave 'as those who are engaged in sacred service' (Tit. 2:3, M.R. Vincent 'Word Studies In The N.T.'). One of the commonest allusions is the idea of ministry. Time and again, the Old Testament speaks of the priests ministering in the priest's office. The priests are specifically called God's ministers (Is. 61:6; Jer. 33:21; Ez. 45:4; Joel 1:9,13; 2:17). The early Christians would have heard and read many of the New Testament references to ministers and ministry as invitations to see themselves as a new priesthood. The Lord said that we should aim to be a minister, a priests, to every one of our brethren, not expecting them to minister to us, but concentrating on ministering to them (Mt. 20:26). This is exactly against the grain of our nature, and also of the concept of religion we find in the world. People expect to have others spiritually ministering to them. They expect a priest-figure to do all their thinking for them. But our Lord said that we are each other's priests, we're not here to be ministered ('priest-ed') to, but to minister, and give our lives in service to each other. There are some concrete examples of ministering. Paul speaks of preaching God's word, both in the world and to brethren and sisters, as ministering (Col. 1:23,25; 1 Cor. 9:13). He saw himself as a minister of the Gospel " that the offering up of the Gentiles might be acceptable" (Rom. 15:16). This is priestly language. Paul saw his efforts for others as preparing a sacrifice. He says that we are all ministers (cp. priests) of God, stewards of the true Gospel, and should act appropriately (1 Cor. 4:1). Others gave money to poorer brethren, and again this is described as ministering, priest-ing (Rom. 15:27; Heb. 6:10). Reminding brethren of basic doctrines they already know is another kind of ministering (1 Tim. 4:16). Indeed, Peter says that we each have something to minister to each other, there is some way in which we can each serve each other (1 Pet. 4:10,11). We must bear one another's burden, as the priesthood bore the burden of Israel's iniquity (Num. 18:1,23). This is the meaning of priesthood.
Mt. 19:27-30 has a series of extended allusions to the fact that we are now the priesthood. The Lord speaks of how His followers will each have left mother, brother etc. to serve Him, referring to how Moses blessed Levi for forsaking these very things so as to God's service (Dt. 33:9). But He also spoke of how they would forsake houses and lands for His sake and the Gospel's- a reference to the way the Levites resigned their right to physical inheritance in the land for the sake of their relationship with God and the work they were called to. In the same way as Moses predicted that the Levites would be materially blessed even now as a result of their dedication (Dt. 33:11), so the Lord made the same promise. And there is no Christian who has heart and soul committed themselves to the Gospel's work, either in the world or amongst their brethren, who has not lived to see the Truth of this definition of priesthood.
Yet the NT not only encourages us to all be priests; but we can even aspire to the High Priesthood, in a certain sense. James 5:16 speaks of the need to pray for one another, that we may be healed. This is an undoubted allusion back to mighty Moses praying for smitten Miriam, and to Aaron staying the plague by his offering of incense / prayer (Num. 16:47). Surely James is saying that every one of us can rise up to the level of High Priest in this sense. Under the Law, the provision for Nazariteship encouraged the average Israelite to enter into the spirit of the High Priest by imposing some of the regulations governing his behaviour upon them. All Israel were bidden make fringes of blue, in conscious imitation of the High Priest to whose spirit they all were intended to attain (Num. 15:38). But we are bidden now " come boldly unto the throne of grace (cp. the mercy seat in the Most Holy)...boldness to enter into the holiest" (Heb. 4:16; 10:19): to do what only the High Priest could do under the Old Covenant. This must have been a huge challenge for the Jewish believers to rise up to. The context of Heb. 10 encourages us to enter the Holiest and " consider one another" . The High Priest entered the Holiest in order to make atonement for Israel, not just to bask in the fact he was allowed in there. And so with us. The marvellous fellowship with the Father which we are permitted in Christ, the entry into the Holiest, is not just for the sake of it; it is so we can do something for others. I am not suggesting, of course, that in any way we replace the one and only High Priest, the Lord Jesus. But because we are in Him we therefore in some ways share His honours and His work. The idea of eating the bread of the sacrifices would likewise have appeared strange in a first century context: it was as if the whole brotherhood (and sisterhood) were being invited to see themselves as priests. But in His last message, the Lord went further: He promised that those who overcome will eat of the hidden manna, concealed in the Most Holy: as if to say that we will ultimately rise up to and exceed the glory of the High Priests who saw that bread once a year. If we enter in at the door of the sheepfold, we will go in and out (a NT idiom for leadership) and find pasture (Jn. 10:9). This may mean that the sheep becomes a shepherd, searching for good pasture for others, leading others, grasping the meaning of priesthood, all as a result of our experience of the good shepherd.