Answer
The Holy Spirit existed and was active in the Old Testament. The Holy Spirit gave gifts to his servants in the Old Testament in a similar way to the gifts he gave in the New Testament. For example, to the people who established a tabernacle, he gave them wisdom to know how to establish it. This tabernacle resembles the presence of our Lord on earth. So, he has infinite wisdom and can give wisdom to his servants. We see also in the book of Judges how he gave power to the judges and also to the kings to accomplish their roles to shepherd and protect the people. We also see some other activities of the Holy Spirit in the Old Testament. In Isaiah 63 we read about the role of the Holy Spirit. Here, the prophet is referring to the exodus and says in verse 10: "But they rebelled—he is talking about the people of Israel—rebelled and grieved his Holy Spirit." So, they grieved his Holy Spirit. We read the same words in the epistle to the Ephesians chapter 4: "Do not grieve the Holy Spirit of God." This emphasizes that the Holy Spirit is a person and affirms that he is the person of God who grieves when his people rebel against him. In the same context, again in Isaiah 63 he says: "He put in the midst of them his Holy Spirit" (verse 11). God put in the midst of the people his Holy Spirit. This Spirit resembles the presence of God. He is not an angel, but God himself dwells in the midst of his people. This reminds us of the dwelling of the Holy Spirit in the New Testament; it has its parallel in the Old Testament. So, the dwelling of the Holy Spirit in the midst of the people proves that this is God.