The gifts of the Spirit appear to have ceased with the death of the Apostles (including Paul) as they were the only ones who could pass on the gifts by the laying of hands. For example:
“These they set before the apostles, and they prayed and laid their hands on them.” (Acts 6:6)
“And when Paul had laid his hands on them, the Holy Spirit came on them, and they began speaking in tongues and prophesying.” (Acts 19:6).
“For this reason I [Paul] remind you to fan into flame the gift of God, which is in you through the laying on of my hands” (2 Timothy 1:6).
In Acts 8, we find that Simon tried to buy this power of passing on the Spirit but found that it was something only the apostles could do.:
“Now when Simon saw that the Spirit was given through the laying on of the apostles’ hands, he offered them money, saying, “Give me this power also, so that anyone on whom I lay my hands may receive the Holy Spirit.” (Acts 8:18-19).
The Apostle Paul said that the gifts would finish, in 1 Corinthians 13:8:
“Love never ends. As for prophecies, they will pass away; as for tongues, they will cease; as for knowledge, it will pass away.”
The Spirit gifts were given for a purpose — to help convince people that the gospel message was true (Mark 16:15,17-18) and establish the early Christian church (Eph. 4:8-14). Once Christianity was established (Eph. 4:13 — ‘mature’, perfect), the gifts passed away (1 Cor. 13:10).
We don’t need the Spirit gifts today because we have the full revelation of God in the Bible to guide us (2Tim. 3:16-17) — it has everything we need to make us ‘competent, equipped for every good work’. In the times of the New Testament, they only had the Old Testament and a few of the books of the New Testament as they were written. When the Bible was finally completed, the gifts ceased to be.
In Hebrews 6:4-5, the author speaking of the Spirit gifts says that they were a taste of the powers of the age to come:
“For it is impossible, in the case of those who have once been enlightened, who have tasted the heavenly gift, and have shared in the Holy Spirit, and have tasted the goodness of the word of God and the powers of the age to come …”.
So we can expect a new age of Spirit gifts when Jesus returns and establishes his kingdom.