This is a great question. We should pray for all of our leaders—both church leaders and government leaders. I suspect, in the circumstances we Americans find ourselves these days, the thinking behind the question may be more about civil and political leaders.
I recently completed a series on Romans for Ligonier, and I had to do some thinking about Romans 13. It came home to me how strongly Paul talks about civic leaders as servants of God and ministers of God. I think Paul, like Peter in 1 Peter 2, observed that some Christians in their first-century context had begun to say: “Since I am free in Christ, I really don’t have to pay much attention to civic leaders. I am free in Christ and therefore transcend obligations to the unbelieving civic authorities.” Both Paul and Peter make strong arguments against that fundamentally wrong way of thinking. Our freedom in Christ does not dissolve our obligations of obedience to the civil authorities God has placed over us.
Our prayers for those civil authorities over us ought to be serious, sincere, and earnest. They ought to be prayers that the civil authorities would fulfill the responsibilities God has given them to do justice and promote real justice in the world. They are not to serve themselves, their own interests, or the interests of the crowd of people who support them. It’s interesting that in the Scriptures, and especially in the Psalms, there exists a particular obligation for rulers to protect the poor and the weak. We ought to be praying for civic leaders to fulfill that obligation. Where we feel that civic leaders may not be Christians in the way they’re fulfilling their office, we should pray for their conversion. Those are all areas in which we ought to be earnestly in prayer. One of the ways in which we honor our civic leaders is by taking their needs before the Lord.
In terms of church leaders, we ought to be praying for pastors, elders, and deacons to be faithful to the Scriptures and faithful to their calling to lead the people of God in their churches.