Without question there is a marked difference in the Spirit’s work this side of the cross and the ascension of Christ, but there is also a remarkable amount of continuity in his work throughout the history of redemption. Perhaps it is more a case of degree as opposed to kind.
Here are some works of the Spirit we see in the Old Testament that have continuity with his work in these New Covenant days. We see the Spirit as the executive of saving activity (Is 63.7-14); provides access to God’s presence as the Spirit of God filled the tabernacle/temple (bringing us into the presence of God is a much broader theological theme and is in relation to the kingdom of God; I don’t think you can really separate the two); gives new life/heart circumcision/born again (Deut 30.6, John 3.1-15); involved in bringing God’s word to the people (via prophets, 1 Pet 1.11, etc.). A few thoughts on the Spirit’s ongoing work in and among the people of God.