Quite a lot, actually, and it’s very affirming. Take for example, the Apostle Paul’s words to the early church in Rome:
"We have different gifts, according to the grace given to each of us. If your gift is prophesying, then prophesy in accordance with your faith; if it is serving, then serve; if it is teaching, then teach; if it is to encourage, then give encouragement; if it is giving, then give generously; if it is to lead, do it diligently; if it is to show mercy, do it cheerfully." (Romans 12:6-8)
The call of God is connected to gifts that are received from the Holy Spirit. Nothing in this passage connects the gifts and calling of God to a specific gender.
When Paul tells leaders to "lead" diligently, he uses the Greek word "proistamenos" (Romans 12:8). The noun form of this word is "prostatis." In Romans 16:2, Paul refers to Phoebe as a "prostatis." When Paul refers to himself as a "minister of the gospel," he uses the Greek word "diakonos" (Colossians 1:23). Similarly, Phoebe is described by Paul as a “diakonon” in the church of Cenchrea (Romans 16:1).
Priscilla taught a man "the way of God more accurately" (Acts 18:26). The Greek word is "exethento"; this is the same activity Paul engaged in when he explained from the Law and the Prophets that Jesus was the Messiah (Acts 28:23).
Some misinterpret 1 Timothy 2:12 to be saying that women cannot teach men. 1st Timothy was a letter written to the church in Ephesus. Priscilla taught a man “the way of God more accurately” in Ephesus. From chapter 1 through chapter 6 of 1st Timothy, Paul is addressing people who were engaged in “false” teaching. It appears that at least one of these false teachers was "a woman." In 1 Timothy 1:20, however, we see that some of these false teachers were men.
Some also misinterpret 1 Timothy 2:12, to be saying that women may not “exercise authority” over men in the church. However, the word translated “exercise authority” in Latin and English versions of the Bible was repeatedly used in 1st century Greek to refer to someone who was responsible for someone's death. In the writing of Philo of Alexandria, for example, being an “authentes” was connected to causing death by embracing a false knowledge (“gnosis”) of God (see Philo’s “The Worse Attacks the Better").
Using similar language, Paul prohibits “a woman” from “authentein andros,” possibly referring to a false teaching that would be responsible for the death of a man. The woman is compared to Eve in 1 Timothy 2:13-14, who was deceived and gave the forbidden fruit to her husband, who ate it and then died. Early Gnostics completely misunderstood the creation account found in Genesis. They taught that the serpent was a messenger from God, and that Eve did a good thing when she shared divine “gnosis” with Adam. In 1st Timothy 6:20, Paul warns Timothy to guard the gospel against profane babblings that are falsely called “gnosis.”
Women—like men—proclaimed the gospel message, taught spiritual truths about Jesus Christ, and provided leadership to the early church. These are the roles performed by a person commonly referred to as a "pastor," though that particular title is not explicitly found in the Greek New Testament. In Greek, we see church leaders referred to metaphorically as "poimenas" (shepherds) in Ephesians 4:11. The Latin equivalent is "pastores," and this is likely where the title “pastor” comes from. Literally, being a “shepherd,” however, was by no means an exclusively “male” occupation. Rachel, for example, is described as a “shepherd” in Genesis 29:9. As far as metaphors go, poimenas is certainly a fitting description of a “pastoral” role. This role, however, was by no means limited exclusively to men.
When the church became the official state religion of the Roman Empire, centuries after Christ’s earthly ministry, Rome's patriarchal laws and customs began to strongly influence the institutional leadership of the church. Human custom began to supersede the call and gifting of the Holy Spirit, and leadership eventually became exclusively male. Today some still confuse this fallen human tradition with the will of God; this hinders the gospel, harms the body of Christ and grieves the heart of God.
Does the New Testament support women being “pastors” in the church? Yes, when read in its original language and context, and not confused with fallen human traditions, it most certainly does.