At first, Prince Hal is set in opposition to King Henry IV's Lord Chief Justice (LCJ), the guy appointed to uphold "the majesty and power of law and justice" (5.2.9). Apparently, the LCJ once threw the prince in the slammer for boxing him on the ears. This is just an old fashioned way of saying Hal once smacked the Lord Chief Justice upside his head and has been at odds with the guy ever since. After King Henry IV dies and Prince Hal officially becomes King Henry V, the LCJ is worried that the new monarch will punish him.
When Hal becomes the King Henry V, he needs a trusty advisor and new BFF, especially since being friends with the degenerate Falstaff is now out of the question. This job calls for the Lord Chief Justice, wouldn't you say? The Lord Chief Justice seems to be the only honest and impartial guy in the entire kingdom, which is why Hal thinks it's a good idea to have him on his side. He says to the LCJ "My voice shall sound as you do prompt my ear / And I will stoop and humble my intents / To your well-practiced wise decision" (5.2.4). In other words, from here on out, the LCJ has got the king's ear. Hal also embraces the LCJ as a "father" figure, which means that the Lord Chief Justice has taken the place of Falstaff, who was Hal's surrogate father figure in Henry IV Part 1.