I’d like to sketch an answer to this question under two headings:-

(a) His personality:-

This becomes clear in the NT, as in Jesus’ promise of ‘another Counsellor’, Jn 14:16, and the fact that the Spirit:-

1. Speaks, Acts 1:16; 8:29; 10:19; 11:12; 13:2; 28:25.
2. Teaches, Jn 14:26.
3. Witnesses, Jn 15:26.
4. Searches, 1 Cor 2:11.
5. Determines, 1 Cor 12:11.
6. Intercedes, Rom 8:26f.
7. Is lied to, Acts 5:3.
8. Can be grieved, Eph 4:30.
9. Can be insulted, Heb 10:29.
10. Is referred to as ‘he’, Jn 16:13.

(b) His divinity:-

1. Lying to the Spirit is lying to God, Acts 5:3f.
2. Linked with the Father and Son in benedictions, 2 Cor 13:14; Rev 1:4-6; and in the baptism formula, Mt 28:19.
3. Called ‘the seven spirits’, Rev 1:4; 3:1; 4:5; 5:6, partly because seven is a number of divine perfection and partly because the Spirit ministers in his fullness.
4. Called the Spirit of the living God, 2 Cor 3:3; 1 Pet 4:14.
5. Sovereignty is ascribed to him, 1 Cor 12:11.
6. Has divine attributes such as omnipresence, Psa 139:7ff; 1 Cor 12:13; omniscience, 1 Cor 2:10; omnipotence, Lk 1:35; Rom 8:11; 15:19.
7. OT refs to God are in the NT shown to be refs to the Holy Spirit, Ex 17:7 w Heb 3:7-9; Isa 6:3,8-10 w Acts 28:25-27; Psa 78:17,21 w Acts 7:51.