“N’avoir qu’à [verbe]” means X can do something himself. This is often a bit judgmental. The presence of “que” implies that the action is easy to do.

“Tu n’as qu’à le manger” = “eat it yourself” (implying “instead of me”)
“Tu n’as qu’à y aller” = “You can go” (instead of asking me to do it)
“Tu n’as qu’à le faire” = “YOU do it”

From le Trésor de la Langue Française, entry avoir III, A, 2:

N’avoir qu’à + inf.Il suffit de…

i.e., n’avoir qu’à followed by an infinitive means “to just have to”. Here, a (poor, literal) translation from French to English could be:

Harry just has to go.