“Spirit of grace” is another name for the Holy Spirit. The writer of the book of Hebrews used it while emphasizing the seriousness of rejecting the grace of God that had been made available through the blood of the new covenant. Grace is another word for the favor that God gives to repentant sinners even though they deserve punishment. It is God’s nature to be gracious; the Holy Spirit, as part of the Trinity, shares the attributes of God.
Spirit of grace in Greek:
To pneuma tēs charitos
Strong’s Concordance numbers: 4151, 5485
Bible reference: Heb. 10:29
Anyone who rejected the law of Moses died without mercy on the testimony of two or three witnesses. How much more severely do you think someone deserves to be punished who has trampled the Son of God underfoot, who has treated as an unholy thing the blood of the covenant that sanctified them, and who has insulted the Spirit of grace? (Hebrews 10:28-29)
The Old Testament has a similar name for the Holy Spirit: Spirit of grace and supplication. The New Testament calls God the Father the God of all grace.