Luke 6:12-16 (also Mk. 3:13-19)

12 It was at this time that He went off to the mountain to pray, and He spent the whole night in prayer to God. 13 And when day came, He called His disciples to Him and chose twelve of them, whom He also named as apostles: 14 Simon, whom He also named Peter, and Andrew his brother; and James and John; and Philip and Bartholomew; 15 and Matthew and Thomas; James the son of Alphaeus, and Simon who was called the Zealot; 16 Judas the son of James, and Judas Iscariot, who became a traitor.

Here we may note that Peter is named first. And in Matthew 10:2 it even says, “The first, Simon…” Moreover, in the list of apostles in Mark 3:16-19 and in Acts 1:13, Peter is listed first. Hence, not only does Peter always act as the leader, he is pointed out in Scripture (which is inspired by God) as the appointed leader.