Jamieson, Fausset and Brown on Hebrews 10:21

21. high priest--As a different Greek term (archiereus) is used always elsewhere in this Epistle for "high priest," translate as Greek here, "A Great Priest"; one who is at once King and "Priest on His throne" (Zec 6:13); a royal Priest, and a priestly King.

house of God--the spiritual house, the Church, made up of believers, whose home is heaven, where Jesus now is (He 12:22, 23). Thus, by "the house of God," over which Jesus is, heaven is included in meaning, as well as the Church, whose home it is.