Prince Hal (the star of Henry IV Part 1 and Part 2) doesn't make an appearance onstage in Richard II, but Shakespeare gives him an important shout-out toward the end of this play. Check out this passage, where King Henry IV wonders where his good-for-nothing son has been for the last three months:
Can no man tell me of my unthrifty son?
'Tis full three months since I did see him last;
If any plague hang over us, 'tis he.
I would to God, my lords, he might be found:
Inquire at London, 'mongst the taverns there,
For there, they say, he daily doth frequent,
With unrestrained loose companions,
Even such, they say, as stand in narrow lanes,
And beat our watch, and rob our passengers; (5.3.1)
Uh oh, looks like King Henry IV is already worried about what could happen when his wild-child inherits the English throne and gets his grubby little hands on the crown. Instead of hanging out at the palace and learning the ropes, Prince Hal is out running around with his hoodlum friends, which doesn't exactly instill confidence in Hal's future leadership abilities. This passage is also important because it gives us a little sneak peek into what we can expect from Prince Hal in the sequel, Henry IV Part 1.