Lord Jesus Christ is the (High) Priest Melchizedek
I believe so.
(i) He is the only One without father, mother etc. but existed prior as this verse states regarding Melchizedek followed by Christ’s pre-existence claim in the Gospel too:
“without father, without mother, without genealogy, having neither beginning of days nor end* of life, and being made like to the Son of God, doth remain a priest continually.” (Hebrews 7:3)
“Jesus said to them, “Most certainly, I tell you, before Abraham came into existence, I AM.” (John 8:58)
(ii) Now, being made ‘like to the Son of God’ means He was like the ‘other sons of God’ (describing His revealed form as Melchizedek). These ‘sons of God’ were ‘created dignitaries’ appointed by God as this verse reveals:
“And the day is, that sons of God come in to station themselves by the LORD, and there doth come also Satan in their midst.” (Job 1:6)
(iii) It’s common knowledge that these ‘sons of God’ can appear as ‘man’ when they presented themselves before the children of men as this verse gives such an instance (without which they could not have married women):
“that the sons of God saw that the daughters of men were beautiful; and they took wives for themselves, whomever they chose.” (Genesis 6:2)
So, the account in Genesis when Moses meets Melchizedek and that He’s called a ‘man’ does NOT necessarily prove that He is a ‘mortal human being’.
(iv) Next, His name which means both ‘King of Righteousness’ and ‘King of Peace’ can ‘only’ refer to God (and it can’t be the Father nor the Holy Spirit simply because only the Son can be the Priest):
“For this Melchisedek, King of Salem, Priest of God Most High, who did meet Abraham turning back from the smiting of the kings, and did bless him,
to whom also a tenth of all did Abraham divide, (first, indeed, being interpreted, ‘King of Righteousness,’ and then also, King of Salem, which is, King of Peace,)” (Hebrews 7:1 – 2)
(v) Now, a common fallacy is to *think* that ‘another priest’ means ‘another person’ which is NOT necessarily true.
“And it is yet more abundantly most evident, if according to the similitude of Melchisedek there doth arise another Priest,” (Hebrews 7:15)
In fact, ‘another Priest’ means ‘a different priest with respect to His Manifestation’. What’s the difference?
As Melchizedek (His revealed form to Abraham), the Lord is yet to function as a Priest to ‘take away sins by the Sacrifice of Himself’. Now, after being revealed in the Flesh as Lord Jesus Christ, His Priestly Role fulfills it.
Melchizedek (His Manifestation is revealed as the ‘Son of God’ only).
Lord Jesus Christ (His Manifestation includes the above and He is revealed in the Flesh too as the ‘Son of Man’).
(vi) Now, since Melchizedek refers only to His Manifestation as the ‘Son of God’, His coming in the Flesh, followed by His Death & Resurrection accounts for Him to be ‘another Priest’ according to the order of Melchizedek to the age with the power of endless life.
“who came not according to the law of a fleshly command, but according to the power of an endless life,
for He doth testify — ‘Thou [art] a Priest — to the age, according to the order of Melchisedek;’” (Hebrews 7:16 – 17)
*Remark: Some may say that when Lord Jesus died on His Cross, His life ‘ended’ and thus the criteria ‘nor end of life’ (in Hebrews 7:3 above) cannot refer to Him. This is a ‘conceptual error’.
Also, this is a shallow argument since His Life did ‘not’ end when He died for even Death couldn’t hold Him as it’s written:
“whom God did raise up, having loosed the pains of the death, because it was not possible for Him (Lord Jesus) to be held by it,” (Acts 2:24)
That is, His Death was ‘not the end’ (so, no ‘end of life’) because it was to be followed by His Glorious Resurrection!
Remember, ‘end of life’ refers to ‘anyone’ who has ‘died and went into the afterlife’ (Hades or Paradise) but has ‘never’ Resurrected. Only Lord Jesus Christ Resurrected (proving that He has ‘no’ end of life) and that in Him, others may live too:
“Who (Lord Jesus Christ) is at the right hand of God, having gone into heaven, after angels and authorities and powers had been subjected to Him.” (1 Peter 3:22)