In the Reformed community we would say that there is nothing Biblical requiring it. However for a number of practical reasons we generally require a minister. (Traditionally that is expressed as "church order".) Some Reformed churches allow specially trained elders where there aren't enough pastors available. I have no problem with that.
But these are for normal situations. You could imagine odd emergency situations where a Christian community might authorize someone else. On the other hand, in a Reformed community I'd expect that in most situations that person would be elected an elder.
Westminster Directory:
As there were in the Jewish church elders of the people joined with the priests and Levites in the government of the church; so Christ, who hath instituted government, and governors ecclesiastical in the church, hath furnished some in his church, beside the ministers of the word, with gifts for government, and with commission to execute the same when called thereunto, who are to join with the minister in the government of the church. Which officers reformed churches commonly call Elders.
The pastor is an ordinary and perpetual officer in the church, prophesying of the time of the gospel.
First, it belongs to his office,
To pray for and with his flock, as the mouth of the people unto God, Acts vi. 2, 3, 4, and xx. 36, where preaching and prayer are joined as several parts of the same office. The office of the elder (that is, the pastor) is to pray for the sick, even in private, to which a blessing is especially promised; much more therefore ought he to perform this in the publick execution of his office, as a part thereof.
To read the Scriptures publickly; for the proof of which,
1. That the priests and Levites in the Jewish church were trusted with the publick reading of the word is proved.
2. That the ministers of the gospel have as ample a charge and commission to dispense the word, as well as other ordinances, as the priests and Levites had under the law, proved, Isa. lxvi. 21. Matt. xxiii. 34. where our Saviour entitleth the officers of the New Testament, whom he will send forth, by the same names of the teachers of the Old.
Which propositions prove, that therefore (the duty being of a moral nature) it followeth by just consequence, that the publick reading of the scriptures belongeth to the pastor's office.
To feed the flock, by preaching of the word, according to which he is to teach, convince, reprove, exhort, and comfort. To catechise, which is a plain laying down the first principles of the oracles of God, or of the doctrine of Christ, and is a part of preaching. To dispense other divine mysteries. To administer the sacraments.
To bless the people from God, Numb. vi. 23, 24, 25, 26. Compared with Rev. i.4, 5, ( where the same blessings, and persons from whom they come, are expressly mentioned,) Isa. lxvi. 21, where, under the names of Priests and Levites to be continued under the gospel, are meant evangelical pastors, who therefore are by office to bless the people. To take care of the poor. And he hath also a ruling power over the flock as a pastor.
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