Translation:When are you going to put on your new shirt?
Ponerse = to put on (an item of clothing)
Llevar or llevar puesto = to wear an item of clothing
Llevarse an item of clothing = To steal it!
I have seen poner used for to wear as well. Either one of them should be correct.
Nope. The se pronoun ending does not go with 2nd person singular, which you used for the verb and the possessive (tu). Remember that the infinitive of the verb if you look it up in the dictionary always ends in se but that ending has to change to match the rest of the sentence. So this has to be ponerte.
BUT... if you want to use the formal "you" then you could say Cuándo usted va a ponerse su camisa nueva.