In Old Testament times, the Holy Spirit was "hovering over the face of the waters", He was ON the prophets, He was WITH Yahweh's people, He WENT BEFORE them, He CAUSED King Saul to prophesy, etc. He was called, the Ruach Ha Kodesh in Hebrew--the "breath of God". But, He was not IN them--that will not happen until they see their Messiah Jesus, coming in the clouds of heaven and they say, "Blessed is He who comes in the name of the Lord!" Zechariah 12:10 pictures this moment. In Ezekiel 37:14, we are told that (what was then) "in the distant future" Gog (a word that is a generic term for all of Israel's foes) would conquer them like a cloud (in the time of "Jacob's trouble"--aka the Tribulation) but that the Lord God would preserve a remnant of them through it and that they would be filled with God's Spirit and brought into the new Messianic Kingdom (aka--the Millennial Kingdom).
Jesus, and His body, the Church is the "First Fruits" and we have already been given the indwelling Holy Spirit (in part, to make Israel jealous). After the Church departs in the Rapture, the Holy Spirit will still be here, because faith is made possible through His convicting power. Some say that He will leave with the Church but, I'm guessing that His work will become more as it was in Old Testament times. I suspect that is why those who convert after the Church is gone, are at risk of the "2nd death"--they will not have the (eternal-life-conferring) permanent indwelling presence of the Holy Spirit until they embrace their Messiah who comes in the clouds to rule and reign "with a rod of iron".