Objection 1. It would seem that the effect of the priesthood of Christ pertained not only to others, but also to Himself. For it belongs to the priest's office to pray for the people, according to 2 Maccabees 1:23: "The priests made prayer while the sacrifice was consuming." Now Christ prayed not only for others, but also for Himself, as we have said above (Question 21, Article 3), and as expressly stated (Hebrews 5:7): "In the days of His flesh, with a strong cry and tears He offered [Vulgate: 'offering'] up prayers and supplications to Him that was able to save Him from death." Therefore the priesthood of Christ had an effect not only in others, but also in Himself.
Objection 2. Further, in His passion Christ offered Himself as a sacrifice. But by His passion He merited, not only for others, but also for Himself, as stated above (19, 3,4). Therefore the priesthood of Christ had an effect not only in others, but also in Himself.
Objection 3. Further, the priesthood of the Old Law was a figure of the priesthood of Christ. But the priest of the Old Law offered sacrifice not only for others, but also for himself: for it is written (Leviticus 16:17) that "the high-priest goeth into the sanctuary to pray for himself and his house, and for the whole congregation of Israel." Therefore the priesthood of Christ also had an effect not merely in others, but also in Himself.
On the contrary, We read in the acts of the Council of Ephesus [Part III, ch. i, anath. 10]: "If anyone say that Christ offered sacrifice for Himself, and not rather for us alone (for He Who knew not sin needed no sacrifice), let him be anathema." But the priest's office consists principally in offering sacrifice. Therefore the priesthood of Christ had no effect in Himself.
I answer that, As stated above (Article 1), a priest is set between God and man. Now he needs someone between himself and God, who of himself cannot approach to God; and such a one is subject to the priesthood by sharing in the effect thereof. But this cannot be said of Christ; for the Apostle says (Hebrews 7:25): "Coming of Himself to God, always living to make intercession for us [Vulgate: 'He is able to save for ever them that come to God by Him; always living,' etc.]." And therefore it is not fitting for Christ to be the recipient of the effect of His priesthood, but rather to communicate it to others. For the influence of the first agent in every genus is such that it receives nothing in that genus: thus the sun gives but does not receive light; fire gives but does not receive heat. Now Christ is the fountain-head of the entire priesthood: for the priest of the Old Law was a figure of Him; while the priest of the New Law works in His person, according to 2 Corinthians 2:10: "For what I have pardoned, if I have pardoned anything, for your sakes have I done it in the person of Christ." Therefore it is not fitting that Christ should receive the effect of His priesthood.
Reply to Objection 1. Although prayer is befitting to priests, it is not their proper office, for it is befitting to everyone to pray both for himself and for others, according to James 5:16: "Pray for one another that you may be saved." And so we may say that the prayer by which Christ prayed for Himself was not an action of His priesthood. But this answer seems to be precluded by the Apostle, who, after saying (Hebrews 5:6), "Thou art a priest for ever according to the order of Melchisedech," adds, "Who in the days of His flesh offering up payers," etc., as quoted above (Objection 1): so that it seems that the prayer which Christ offered pertained to His priesthood. We must therefore say that other priests partake in the effect of their priesthood, not as priests, but as sinners, as we shall state farther on (ad 3). But Christ had, simply speaking, no sin; though He had the "likeness of sin in the flesh [Vulg.,: 'sinful flesh'," as is written Romans 8:3. And, consequently, we must not say simply that He partook of the effect of His priesthood but with this qualification--in regard to the passibility of the flesh. Wherefore he adds pointedly, "that was able to save Him from death."
Reply to Objection 2. Two things may be considered in the offering of a sacrifice by any priest--namely, the sacrifice itself which is offered, and the devotion of the offerer. Now the proper effect of priesthood is that which results from the sacrifice itself. But Christ obtained a result from His passion, not as by virtue of the sacrifice, which is offered by way of satisfaction, but by the very devotion with which out of charity He humbly endured the passion.
Reply to Objection 3. A figure cannot equal the reality, wherefore the figural priest of the Old Law could not attain to such perfection as not to need a sacrifice of satisfaction. But Christ did not stand in need of this. Consequently, there is no comparison between the two; and this is what the Apostle says (Hebrews 7:28): "The Law maketh men priests, who have infirmity; but the word of the oath, which was since the Law, the Son Who is perfected for evermore."
Source: Summa Theologica (New Advent)