St. Bede writes (as quoted in St. Thomas Aquinas's Golden Chain commentary on Luke 22, lesson 4):
Thus then was our Lord the approver of the legal Passover; and as He taught that it related to the figure of His own dispensation, He forbids it henceforth to be represented in the flesh.* Therefore He adds, "For I say to you, I will not any more eat thereof; until it be fulfilled in the kingdom of God". That is, I will no more celebrate the Mosaic Passover, until, being spiritually* understood, it is fulfilled in the Church. For the Church is the kingdom of God; as in Luke [17:21], "The kingdom of God is within you." Again, the ancient Passover, which He desired to bring to an end, is also alluded to in what follows; "And he took the cup, and gave thanks, and said, Take you, &c." For this gave He thanks, that the old things were about to pass away, and all things to become new.
St. Cyril of Alexandria, sermon 151 on Luke 22:7-16:
"But I will not eat of this Passover until it is fulfilled in the kingdom of God." And in this again Christ utters a profound and mysterious truth, of which He Himself, however, reveals to us the meaning. For it is His custom to give the name of "the kingdom of heaven" to justification by faith, to the cleansing that is by holy baptism and the participation of the Holy Spirit, and to the offering of spiritual service, now rendered possible by the entering in of the gospel laws. But these things are the means of our being made partakers of the promises, and of our reigning together with Christ: and therefore He says, "I will no more draw near to such a Passover as this," one namely that consisted in the typical eating,*—for a lamb of the flock was slain to be the type of the true Lamb,—"until it is fulfilled in the kingdom of God:" that is, until the time has appeared in which the kingdom of heaven is preached. For this is fulfilled in us, who honor the worship that is superior to the law, even the true Passover; nor is it a lamb of the flock which sanctifies those who are in Christ, but Himself rather, being made a holy sacrifice for us, by the offering of bloodless oblations, and the mystical giving of thanks, in which we are blessed and quickened with life. For He became for us "the living bread that came down from heaven, and gives life to the world:" by Whom and with Whom to God the Father be praise and dominion, with the Holy Spirit, for ever and ever. Amen.
*Thus, it's a spiritual food.
cf. Jn. 4:34: "My meat is to do the will of him that sent me"