Answer: Paul and Barnabas appointed elders for the
disciples in each church they visited in the area of Lystra,
Iconium and Antioch, (verses 21 and 23).
MORE INFORMATION AND/OR OTHER SCRIPTURE REFERENCES:
From The Acts of the Apostles From Jerusalem to Rome
by Wayne Jackson:
As Paul and Barnabas visited the various congregations they
had established earlier, they appointed elders in each
congregation. These "elders" were the shepherds
or overseers of the individual churches. The qualifications
for this work are set forth in 1 Timothy 3 and
Titus 1. Most likely, following the principle
pursued in Acts 6, the Christians selected their own
elders, and Paul and Barnabas formalized the procedure by an
official "appointment." If one wonders how elders
could be appointed so soon, when a "novice" is
forbidden such an endowment (1 Timothy 3:6), it
should be remembered: 1) Some of these men were likely Jews,
trained in the Old Testament, and thus already spiritually mature
persons (cf. Larkin, 217); 2) Paul almost certainly would have laid
hands on these men, imparting spiritual gifts, which would qualify
them for the noble task to which they had agreed.
Paul also directed Titus how he should appoint elders in the
churches of Christ on the island of Crete:
Titus 1:5: "The reason I left you
in Crete was that you might straighten out what was left unfinished
and appoint elders in every town, as I directed you."