At that time Herod the tetrarch heard of the fame of Jesus,
Note 1 at Mt 14:1: Matthew's statement "at that time" simply means that Herod heard of the fame of Jesus during His tour of Galilee that Matthew had just recorded. Mark and Luke spoke of Herod hearing about Jesus after He had sent out His twelve disciples into all the villages of Galilee, but that also took place during the same tour of Galilee that Matthew was describing, so there is no discrepancy between the accounts.
Mark's and Luke's linking of Herod hearing about Jesus with the sending forth of the twelve disciples would imply that these twelve disciples did much to publicize the ministry of Jesus. This was the reason that on another occasion, Jesus sent seventy of His disciples ahead of Him into every city and place where He was planning to go (Lu 10:1). He was publicizing His coming so that everyone would have the opportunity of seeing and hearing Him.
Note 2 at Mt 14:1: The word "tetrarch" means "the ruler of a fourth part of a country" (Strong's Concordance). It was adapted by the Romans to designate many petty rulers whom they chose not to dignify with the title of king. However, in Herod Antipas' case, the title was true in its original meaning. According to Josephus, Caesar Augustus gave one half of the realm of Herod the Great to Archelaus, Herod the Great's son (see note 3 at Lu 3:1), and he divided the other half between Herod Antipas (mentioned here) and his brother Philip (The Antiquities of the Jews, Book 17, Chapter 11, Section 4; and War of the Jews Book 2, Chapter 6, Section 3).