The NT gives a "personality" to the HS, it is a "he" and not an "it" and He teaches, feels, rejoices and is sad.
The HS is not just God's HS, but also Jesus's:
2Corinthians3:12-18
12 Therefore, since we have such a hope, we are very bold. 13 We are not like Moses, who would put a veil over his face to keep the Israelites from gazing at it while the radiance was fading away. 14 But their minds were made dull, for to this day the same veil remains when the old covenant is read. It has not been removed, because only in Christ is it taken away. 15 Even to this day when Moses is read, a veil covers their hearts. 16 But whenever anyone turns to the Lord, the veil is taken away. 17 Now the Lord is the Spirit, and where the Spirit of the Lord is, there is freedom. 18 And we, who with unveiled faces all reflect a the Lord’s glory, are being transformed into his likeness with ever-increasing glory, which comes from the Lord, who is the Spirit.
Notice that only Christ can take it away( the veil) and that anyone that turns to the Lord (Christ) has the veil taken away, now notice that "the Lord is Spirit" and the "Lord, who is THE spirit".
In all of Paul's writings he makes it clear that The Lord = Jesus Christ.