Question: "What is the duty / role of a pastor's wife?"
Answer: The Bible does not address the involvement of the pastor's wife in any ministry. In other words, it depends upon the denomination, the individual church within a denomination, the church board, and the pastor and his wife to determine how active the pastor's wife should be. The main area of responsibility for any wife is to support and be submissive to her husband (Ephesians 5:22-24). However, if the Lord calls a man into the ministry, He calls the whole man, and that includes the man's wife and his family.
The Apostle Paul in 1 Timothy 3 gives us the qualifications of a "bishop" or what we call a pastor, and in verse 4 we see the following: "one who rules his own house well, having his children in submission with all reverence." "Rules well" is an idiom for being a biblical husband with a submissive wife and children that love and respect him. The pastor who is the head of his home will be more successful as a leader in the church, and of course this means that his wife is his helper in the ministry of the home as well as the church. The ministry is a partnership in all areas of life and not just in the home life.
The wife does not do the work of the pastor, but the pastor and his wife are a team who are yoked together to do God's work. Too few recognize the reality of this and want to put the pastor's wife in a box and relegate her to keeping the home fires burning and prayer support for her husband. That certainly is her responsibility, but quite often the pastor's wife has gifts that can and should be used in the ministry. On the other hand, there are women whose husbands are pastors and they see it as "his" ministry and do not enter in to the work in any way. There should be a good balance between these two ideas with the goal of bringing glory to God in all things. An active, outgoing pastor's wife is a valuable asset to any church in today's climate of apathy to the things of God.