In His ascension Christ is the High Priest according to the order of Melchisedec, without father, without mother, without genealogy, having neither beginning of days nor end of life (Heb. 5:10; 7:3; 8:1). As the eternal Son of God, as the perpetual High Priest, Christ has no genealogy (John 1:1). This is His divine aspect. But as the Son of Man He does have a genealogy (Matt. 1:1-17; Luke 3:23-38). His divinity as the Son of God constitutes Him as our eternal High Priest, so He can pray for us both in heaven and in us.
In His ascension Christ is the Minister of the new covenant (Heb. 8:2) to minister all the riches of the bequests of the New Testament. A testament is a legal, official agreement full of bequests. One bequest of the New Testament is the forgiveness of sins. The following bequest is the giving of the divine life that we may be born again to be God's sons. These are just two of the many bequests in the new testament. A bequest is an item of the promised things given according to the testament, the legal, official agreement. God's forgiving of our sins is His fulfilling of one of the bequests which Christ's death has bought for us. God gave us His life that we could be born again. This is another fulfillment of a bequest in the new testament. All the items of the blessings of the new testament are bequests, and Christ is the Minister of the riches of these bequests.
Not only is Christ a Minister to minister the riches of all the bequests to us, but also He is the Mediator, the Executor, to execute all the bequests of the new testament bequeathed to us by His death (Heb. 8:6).
Christ is the surety of the better covenant (Heb. 7:22). This means that He is the guarantee and the pledge of the new covenant for its fulfillment. The Lord is the Guarantor and also the guarantee of the new covenant. He is the surety, the pledge, that everything in this covenant will be fulfilled.