Mark records that the Herodians 1 were complicit in a plot to destroy Jesus:
And the Pharisees went forth, and straightway took counsel with the Herodians against him, how they might destroy him.
-- Mark 3:6 (KJV)
It is recorded both in Matthew and Mark that the Herodians 1 were sent to try to entangle/catch Jesus in his talk/words:
15Then went the Pharisees, and took counsel how they might entangle him in his talk. 16And they sent out unto him their disciples with the Herodians, saying, Master, we know that thou art true, and teachest the way of God in truth, neither carest thou for any man: for thou regardest not the person of men.
-- Matthew 22:15-16 (KJV)
And they send unto him certain of the Pharisees and of the Herodians, to catch him in his words.
-- Mark 12:13 (KJV)
Mark records, also, that Herod was somewhat of a lunatic, admitting to having killed John the Baptist on a whim, and imagining Jesus to be John reincarnated,:
14And king Herod heard of him; (for his name was spread abroad:) and he said, That John the Baptist was risen from the dead, and therefore mighty works do shew forth themselves in him.
15Others said, That it is Elias. And others said, That it is a prophet, or as one of the prophets. 16 But when Herod heard thereof, he said, It is John, whom I beheaded: he is risen from the dead.
-- Mark 6:14-16 (KJV)
Mark records Jesus as saying of Herod:
... Take heed, beware of the leaven of the Pharisees, and of the leaven of Herod.
-- Mark 8:15 (KJV)
Herod felt threatened by Jesus, which is the clear implication of the introductory words to the question put to Jesus by the Herodians, "Master, we know that thou art true, and teachest the way of God in truth, neither carest thou for any man: for thou regardest not the person of men."
So, when he was taken to Herod, Jesus had absolutely no illusions that his talk/words would have any impact on the outcome of the meeting.
Priestly party under the reign of King Herod and his successors; called by the Rabbis "Boethusians," as adherents of the family of Boethus, whose daughter Mariamne was one of the wives of King Herod, and whose sons were successively made high priests by him.
-- Jewish Encyclopedia