Leaders in the New Testament were chosen in a variety of ways, by different types of church leaders or by consensus.
1) When the choice is between two qualified men, the lot is used. Acts 1:23-26 (See also Proverbs 18:18).
2) By consensus of the church: Acts 6:1-7
3) By divine revelation: Acts 9; Acts 13:2-3; I Timothy 1:18
4) Appointed by an individual in authority (these cases seem to be churches that weren’t well established yet) Acts 16:1-3; 2 Timothy 2:1; Titus 1:5; I Corinthians 4:17
5) By apostle and others choosing together: Acts 14:23; Acts 15:22