If you want a term to describe all of a prince's clothing, I would use finery .
finery Expensive or ostentatious clothes or decoration: officers in their blue, gold, and scarlet finery http://www.oxforddictionaries.com/definition/english/finery
But if you're looking for the 'dress' part of a fairytale prince's clothes, I think it would be tunic .
tunic A loose garment, typically sleeveless and reaching to the knees, as worn in ancient Greece and Rome.
http://www.oxforddictionaries.com/definition/english/tunic
ell.stackexchange.com/users/24987/Graham Nicol
Regalia the special clothes that are worn or objects that are carried at official ceremonies - oxforddictionaries.com
ell.stackexchange.com/users/24861/Lawrence
"Raiment" is often used in this context.
"Tunic" refers to a particular garment; "raiment" is more general.
"Garb" or "dress" (without an article) is a rather drab abstract noun for what a person is wearing.
One does not refer to "a garb".
"A dress" (or using "the" to refer to a particular "garment") means an item of clothing that is normally worn by women.
Thus, "a dress" is inappropriate for a (male) prince, unless he is pretending to be a woman.
ell.stackexchange.com/users/9100/Jasper
If I was writing a story I would refer to the Prince's costume .
ell.stackexchange.com/users/20600/Brian Tompsett - 汤莱恩
If you're looking for a catch-all for what the prince is wearing, consider attire .
The prince's attire was befitting a man of his station.
If you're trying to find what clothes the prince was wearing, that would be dependent on where the prince was and what his local region wore.
ell.stackexchange.com/users/26/corsiKa
Please think of fairytales... What word would you use when you refer to a prince's clothes? Is it a  dress ?
Looking for a word - prince's clothes
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ell.stackexchange.com/users/25744/user25744
Regalia, raiment, finery and attire are all words that may be used to describe a prince's clothes. Regalia, raiment, attire and finery are options.
Regalia, raiment, attire and finery are options.