Let us first look at the two different translations of the following words of the Lord Jesus spoken on the eve of the Cross where He connects the His "blood" or death to a diatheke:
"Then he took a cup, and when he had given thanks, he gave it to them, and they all drank from it. 'This is my blood of the covenant (diatheke), which is poured out for many,' he said to them" (Mk.14:23-24; NIV).
"And he took the cup, and when he had given thanks, he gave it to them: and they all drank of it. And he said unto them, This is my blood of the new testament (diatheke), which is shed for many" (Mk.14:23-24; KJV).
When the Lord Jesus said those words the Greek word diatheke carried with it two different meanings. One of the meanings was in regard to the New Covenant which the LORD promised to the nation of Israel and the other meaning is in regard to the Lord Jesus' Last Will and Testament--the gospel.
On the day of Pentecost the disciples would have understood that the Lord Jesus was speaking about the New Covenant promised to the nation of Israel.
Robert B. Chisholm, Jr, Professor of Old Testament studies at Dallas Theological Seminary, recognizes the fact that on the day of Pentecost the coming of the Millennium remained in view:
"When he (Peter) observed the outpouring of the Spirit on the day of Pentecost he rightly viewed it as the first stage in the fulfillment of Joel's prophecy. Apparently he believed that the kingdom was then being offered to Israel and that the outpouring of the Holy Spirit signaled the coming of the Millennium. However, the complete fulfillment of the prophecy (with respect to both the extent of the Spirit's work and the other details) was delayed because of the Jewish unbelief" [emphasis added] (The Bible Knowledge Commentary; Old Testament, ed. Walvoord & Zuck [Colorado Springs: Chariot Victor Press, 1985], 1421).
Robert L. Saucy recognizes the fact that the New Covenant will be fulfilled in the Millennium, writing that "the connection between the new covenant and the kingdom is evident in Jesus' teaching that his work, which throughout Scripture is intimately identified with the coming of the kingdom, is also the fulfillment of the new covenant. In fact, Jesus expressly tied the fulfillment of the Passover, which he celebrated with his disciples, to the coming of the kingdom of God (Lk 22:16, 18; cf. Mt 26:29; Mk 14:25)" [emphasis added] (Saucy, The Case For Progressive Dispensationalism [Grand Rapids: Zondervan, 1993], 133).
Saucy correctly notes that the Lord Jesus' words in the upper room tied the fulfillment of Israel's New Diatheke to the earthly kingdom:
"...for this is My blood of the covenant, which is poured out for many for forgiveness of sins. But I say to you, I will not drink of this fruit of the vine from now on until that day when I drink it new with you in My Father's kingdom" (Mt.26:28-29).
It was only later after Paul was converted that an understanding of the meaning of the significance of the Lord's Supper for the present dispensation was given. Evidently Paul received a special revelation ("I have received of the Lord...") about the meaning of the Lord's Supper which is not related to the kingdom:
"For I have received of the Lord that which also I delivered unto you, That the Lord Jesus the same night in which he was betrayed took bread: And when he had given thanks, he brake it, and said, Take, eat: this is my body, which is broken for you: this do in remembrance of me. After the same manner also he took the cup, when he had supped, saying, This cup is the new testament in my blood: this do ye, as oft as ye drink it, in remembrance of me. For as often as ye eat this bread, and drink this cup, ye do shew the Lord's death till he come" (1 Cor.11:23-26).
Paul specifically ties communion to the Lord's return to the rapture and not to the kingdom--"ye do shew the Lord's death till he come." We can understand that the glorious body which a believers will receive at the rapture is described as being an "inheritance" and that ties the diatheke of which the Apostle Paul spoke at 1 Corinthians 11:25 to a "testament":
"That we should be to the praise of his glory, who first trusted in Christ. In whom ye also trusted, after that ye heard the word of truth, the gospel of your salvation: in whom also after that ye believed, ye were sealed with that holy Spirit of promise, Which is the earnest of our inheritance until the redemption of the purchased possession, unto the praise of his glory" (Eph.1:12-14).
The believer is sealed with the Holy Spirit and he will remain sealed until he receives the "inheritance" on the day of redemption and that inheritance is a glorious body like the Lord Jesus' glorious body:
"And grieve not the holy Spirit of God, whereby ye are sealed unto the day of redemption...the redemption of our body" (Eph.4:30;Ro.8:23).
So when Paul quoted the Lord Jesus' words on the eve of the Cross the meaning which he placed on the word diatheke was "testament" and not "covenant":
"After the same manner also he took the cup, when he had supped, saying, this cup is the new testament (diatheke) in my blood: this do ye, as oft as ye drink it, in remembrance of me. For as often as ye eat this bread, and drink this cup, ye do shew the Lord's death till he come" (1 Cor.11:25-26; KJV).
John Frahm III wrote that "the use of the word 'testament' confesses more fully the Gospel promises and cross-focused content of Christ's person and work that is distributed Sunday after Sunday in the Divine Service" [emphasis added] (John Frahm III, The Lord's Supper as Christ's Last Will and Testament; http://steadfastlutherans.org/2013/03/the-lords-supper-as-christs-last-will-and-testament/).