Will the Holy Spirit be here during the tribulation? Yes.
There are a lot of people who have been taught that the Holy Spirit will be removed from the earth during the tribulation. This teaching comes from a misunderstanding of 2 Thes 2:7, which says, "For the mystery of iniquity doth already work: only he who now letteth will let, until he be taken out of the way." It is commonly believed that the "he" of this verse is the Holy Spirit, who hinders the work of the mystery of iniquity until the Holy Spirit is taken out of the way at the tribulation.
But this won’t fit the text nor will it fit the cross references. The truth is that the Holy Spirit continues to work here, even during the tribulation. Here’s how you can tell.
First, the mystery of iniquity in verse 7 is a person, he is a man. He has been preventing the world from knowing who he "really" is by "letting [hindering his revelation]" until he is taken out of the way.
This mystery of iniquity will continue to "let" [hinder] until the "man of sin" (v.3) is revealed who is the "son of perdition." The son of perdition is Judas Iscariot, who ascends out of the bottomless pit as the devil incarnate when the mystery of iniquity is taken away. At that time, he won’t be a mystery anymore because that Wicked will be revealed (v.8). For more on this see What is the mystery of iniquity? and Who is "the man of sin," "the son of perdition?" in the weekly question archives.
So, you see that the Holy Spirit is not the one "taken away" before the revelation of the Wicked. It is the mystery of iniquity who is taken away, as in (Rev 17:16-17).
Second, there are a few New Testament references that deal with the tribulation that mention the Holy Spirit. For instance, Mk 13:11 is in the middle of a context that is clearly a reference to the tribulation. Look at v. 14, and notice "the abomination of desolation." In vs. 15-18, the Jews are running for their lives to get away from the antichrist. In v.19 the affliction of that time exceeds all other since creation. In vs. 21-22, false Christs rise up to deceive the people. In v. 13, a man must endure to "the end" to be saved (Matt 24:13, 21). All of these are tribulation references!!
Mk 13:11 says that when a man has to give a testimony before rulers and kings (v.9) during the tribulation, he is not to premeditate on his answer. The reason is that he won’t be doing the talking, the Holy Ghost will. Obviously, then, the Holy Spirit is still working here in the earth during the tribulation (Matt 10:20).
Another text that shows the Holy Spirit is not taken away during the tribulation is Heb 6:4-6. These verses show you what happens when men lose their salvation in the tribulation. It is impossible "to renew them again unto repentance." That is if they lose their salvation they can’t get it back. Now notice what they had before they "lost it." They had the Holy Spirit. Saved people in the tribulation are "made partakers of the Holy Ghost," (v.4).
So, you see from the Bible that the Holy Spirit is active during the tribulation contrary to what many have taught.