Hebrews 7.3 is theological language. In the Old Testament, there is no recorded genealogy or succession recorded for him, but we are not to understand that he was a miraculous or immortal being without birth or death. The significance for the book of Hebrews and the point the author is making is (1) that Melchizedek's was a different type of priesthood from the Levitical priesthood, in which genealogy was of prime importance; (2) Melchizedek had a priesthood independent from the Levitical priesthood. The writer's point is that the Levitical priesthood was inferior to the priesthood of Melchizedek as a way of showing that the Levitical priests and their sacrifices could not atone for sin.

In other words, Melchizedek is presented as a historical person, a special character in the life of Abraham, used as a type here in Hebrews, but otherwise just a normal being. Since he was a priest of the Most High God (Gn. 14.18), we can presume he's in the presence of God with all those who worship the true God.

Where’s Melchizedek? What’s he up to right now? Hebrews 7 describes him as “Without father or mother, without genealogy, without beginning of days or end of life” which sounds rather immortal. What happened with him?