When there are organizational conflicts about congregational politics in a parish, the word "authority" will in most cases be used. Who has authority? Who is obliged to honor that authority? Both sides in a disagreement may find a way to claim authority.
So what is the nature of authority within a Christian community? The quick answer is: I don't know. But let me suggest a few starting points for an investigation of the concept of authority. As always, Scripture is the source and norm for such discussion.
In related passages (Romans 13:1-2 and Titus 3:1), Paul discusses worldly or secular authority. This is to be clearly distinguished from authority within the church. Paul makes this clear in his vocabulary choices: magistrates and principalities.
In the epistle to the Hebrews (13:7 and 13:17), we see ecclesiastical authority discussed. Here it is defined, and we do well to heed these definitions: "leaders, who spoke the word of God to you" and "they keep watch over you as men who must give an account." Here we see three parts of a definition of spiritual authority: first, they speak the word of God; second, they keep watch; third, they do so as men who must give an account.
If I ask, who has spiritual authority in this congregation, the answer is tripartite: those who are speaking the word of God, who are keeping watch, and who are doing so as men who must give an account.
By this definition, anyone who does not speak with word of God (i.e., who does not teach or preach from the Scripture), or who does not keep watch (i.e., as a shepherd protectively nurtures and oversees a flock), or who does not do so with a sense of accountability (i.e., the stewardship of one who realizes that God, the owner of the flock, asks that protective nurture and oversight from His shepherds), is therefore not a spiritual authority, and should therefore not be regarded or recognized as a spiritual authority.
Peter adds to this definition in his first letter, stating that shepherds "serve" (5:2) in way which is "not lording" but rather "being examples."
By Peter's words we then understand that anyone who "lords" (i.e., who exerts positional authority, making demands based merely on his job title, rather than God's written word) is not a spiritual authority. Such "hirelings" work only for money, and run away when suffering appears (John 10:11-14); yet suffering is the school of God to train His saints in righteousness and grow in them the fruit of the Spirit (Galatians 5:22).
These definitions, written clearly in the New Testament, underlie Peter's word (Acts 5:29) that we must obey "God rather than men" - because God has given us definitions of whom we respect as spiritual authorities: God decides who is a spiritual authority. No man can declare himself a spiritual authority. Any self-appointed authority is therefore not an authority.
In chapter 23 of Matthew, Jesus speaks sternly about such self-appointed authorities.
Finally, in Paul's first letter to Timothy (5:19-20), we read that if two or three witnesses can be brought against an elder - reminding us of Deuteronomy 17:6, which writes that we can do nothing based on the testimony of single witness - somebody who claims spiritual authority should be "publicly rebuked."
To re-state my introduction, I write that I do not fully understand what spiritual authority is, or who has it. But these passages of Scripture are the foundation for any doctrine about spiritual authority.