The Holy Spirit bears witness on behalf of Jesus, and those who live in the Spirit must "also witness" (Jn 15:27, our transl). To witness for the risen Jesus is beyond human power. That is why Jesus' witnesses must receive the power of the Holy Spirit (Acts 1:8).
It is both liberating and fearsome to do something beyond our human powers. For example, if Jesus gave you power to walk on water, would you be afraid to take your first steps? (see Mt 14:28-31) Life in the Spirit is by definition beyond our understanding and in some ways beyond our control. This can be a problem for those who base their security on controlling some of the circumstances of life. The Holy Spirit gives us both the occasions to feel fear and the faith to overcome fears.
Moreover, if it is a struggle for someone who is a willing witness for Jesus, imagine how threatened those who oppose or are indifferent to the Holy Spirit may become when the Holy Spirit proves them wrong (Jn 16:8). It is easy to see why the Greek word translated "witness" also can be translated "martyr." So even if Jesus' witnesses are not fearful of the Holy Spirit, they are strongly tempted to be fearful of the world in its opposition to the Spirit.
Do not fear the Holy Spirit. Do not fear those opposed to the Holy Spirit. Be a witness for Jesus, "for the Spirit God has given us is no cowardly spirit" (2 Tm 1:7). Come, Holy Spirit!