Because it's the final play in a four-play cycle, Henry V is always looking over its shoulder (into the historical past and also into the plays that have gone before it). At times, Shakespeare's characters are haunted by their pasts. (Henry must answer for his wild youth and feels compelled to beg God's forgiveness for his father's mistakes.) As Henry looks forward into his future as the King of England (and potentially the King of France), he forges ahead at the expense of leaving old friends (like Falstaff) behind in his wake. Of course, Shakespeare's preoccupation with the past also means that the play is full of shout-outs to the earlier history plays, Richard II, Henry IV Part 1, and Henry IV Part 2.
By refusing to pardon his old pal Bardolph for stealing, King Henry demonstrates that he really has left his wild past behind him.
Although Henry has transformed into a capable king, his wild old ways resurface throughout the play.