Falstaff is a character who never actually appears in this brilliant history play, though news of his death does reach the ears of the characters. We need to remember that Henry V is the third part of a kind of ongoing story, of which Henry IV Parts 1 and 2 are the first and second part. These plays together tell the story of how the youthful Prince Hal slowly develops and becomes King. Prince Hal is shown to be a friend of Falstaff and other such characters as Pistol and Bardolph in the first two plays, and he regularly makes his father despair over his youthful antics. However, when he is crowned king, he has a sudden change of character, and shows how he is a force to be reckoned with. Consider how Ely comments upon this transformation in Act I scene 1:
The strawberry grows beneath the nettle
And wholesome berries thrive and ripen best
Neighbour'd by fruit of baser quality:
And so the prince obscured his contemplation
Under the veil of wildness; which, no doubt,
Grew like summer grass, fastest by night,
Unseen, yet crescive in his faculty.
We can see therefore that by the time of the start of Henry V, Falstaff's influence over Henry has come to an end. Falstaff is one of those fruits "of baser quality" which contributed to the "veil of wildness" which the young prince adopted.