Verses which appear to directly speak to a New Covenant gift of prophecy…
[16] But this is what was uttered through the prophet Joel: [17] “‘And in the last days it shall be, God declares, that I will pour out my Spirit on all flesh, and your sons and your daughters shall prophesy, and your young men shall see visions, and your old men shall dream dreams; [18] even on my male servants and female servants in those days I will pour out my Spirit, and they shall prophesy. [19] And I will show wonders in the heavens above and signs on the earth below, blood, and fire, and vapor of smoke; [20] the sun shall be turned to darkness and the moon to blood, before the day of the Lord comes, the great and magnificent day. [21] And it shall come to pass that everyone who calls upon the name of the Lord shall be saved.’ (Acts 2:16-21 ESV)
[6] Having gifts that differ according to the grace given to us, let us use them: if prophecy, in proportion to our faith; [7] if service, in our serving; the one who teaches, in his teaching; [8] the one who exhorts, in his exhortation; the one who contributes, in generosity; the one who leads, with zeal; the one who does acts of mercy, with cheerfulness. (Romans 12:6-8 ESV)
[8] For to one is given through the Spirit the utterance of wisdom, and to another the utterance of knowledge according to the same Spirit, [9] to another faith by the same Spirit, to another gifts of healing by the one Spirit, [10] to another the working of miracles, to another prophecy, to another the ability to distinguish between spirits, to another various kinds of tongues, to another the interpretation of tongues. (1 Corinthians 12:8-10 ESV)
[28] And God has appointed in the church first apostles, second prophets, third teachers, then miracles, then gifts of healing, helping, administrating, and various kinds of tongues. [29] Are all apostles? Are all prophets? Are all teachers? Do all work miracles? [30] Do all possess gifts of healing? Do all speak with tongues? Do all interpret? (1 Corinthians 12:28-30 ESV)
[39] So, my brothers, earnestly desire to prophesy, and do not forbid speaking in tongues. [40] But all things should be done decently and in order. (1 Corinthians 14:39-40 ESV; note, all of 1Cor 14 connects to this topic)
[11] And he gave the apostles, the prophets, the evangelists, the shepherds and teachers, (Ephesians 4:11 ESV; note, 3:5 makes clear this refers to prophets in Paul’s day, not OT prophets)
[19] Do not quench the Spirit. [20] Do not despise prophecies, [21] but test everything; hold fast what is good. (1 Thessalonians 5:19-21 ESV)